2021
104
Felipe Maciel Ca doso
S a egic and Sel less
In e ac ions: a s udy o
human beha iou
Di ec o /es
Mo eno Vega, Yami
G acia Láza o, Ca los
© Uni e sidad de Za agoza
Se icio de Publicaciones
ISSN 2254-7606
Felipe Maciel Ca doso
STRATEGIC AND SELFLESS INTERACTIONS: A
STUDY OF HUMAN BEHAVIOUR
Di ec o /es
Mo eno Vega, Yami
G acia Láza o, Ca los
Tesis Doc o al
Au o
2020
UNIVERSIDAD DE ZARAGOZA
Escuela de Doc o ado
P og ama de Doc o ado en Física
Reposi o io de la Uni e sidad de Za agoza – Zaguan h p://zaguan.uniza .es
STRATEGIC AND SELFLESS INTERACTIONS
a s udy o human beha iou
elipe maciel ca doso
Oc obe 9,2020

Felipe Maciel Ca doso: S a egic and Sel less In e ac ions: a s udy o
human beha iou , © Oc obe 9,2020
Não sou nada.
Nunca se ei nada.
Não posso que e se nada.
À pa e isso, enho em mim odos os sonhos do mundo.
I am no hing.
I will ne e be any hing.
I couldn’ wan o be some hing.
Apa om ha , I ha e in me all he d eams o he wo ld.
— Tabaca ia, Ál a o de Campos (Fe nando Pessoa)
À Zu, minha mãe, e à Amanda
ABSTRACT
Humans a e unique animals, coope a ing in scale un i alled by any
o he species. We buil socie ies composed o non-kins, and empi ical
esul s ha e shown ha people ha e social-p e e ences and migh be
willing o pe o m cos ly ac ions in he bene i o o he s. On he o he
hand, humans also compe e among hemsel es leading a imes o
nega i e ou comes, such as he o e use o Ea h’s na u al esou ces.
Ye , compe i ion be ween economic agen s unde lies he well unc-
ioning o ma ke s, and i s des abilisa ion – such as in an unbalanced
dis ibu ion o ma ke powe – can ha m ade e iciency. Acco dingly,
analysing how people coope a e and compe e is o p ime impo ance
in he unde s anding o human beha iou , especially conside ing he
impending challenges h ea ening he u u e wel a e o ou socie ies.
In his hesis, we p esen wo ks explo ing people’s beha iou in
social dilemmas – si ua ions in which sel -in e es ed decisions a e a
a iance wi h he social op imum – and in o he s a egic scena ios.
Using he heo e ical amewo k o game heo y, hei in e ac ions
ake place in games abs ac ing hese si ua ions. Speci ically, we pe -
o med beha iou al expe imen s in which people played adap a ions
o common-pool esou ces, public goods, and o he ailo -made games.
Mo eo e , in an a emp o unde s and he exis ence o coope a ion in
humans, we p opose a heo e ical app oach o model i s e olu ion ia
a dynamics o heu is ics selec ion.
We begin by in oducing he heo e ical and empi ical ounda ions
in which his hesis is based upon, namely, game heo y, expe imen al
economics, ne wo k science, and he e olu ion o coope a ion. Subse-
quen ly, we illus a e he p ac ical aspec s o pe o ming expe imen s
using so wa e implemen a ions.
To unde s and people’s beha iou in collec i e ac ion p oblems
– such as clima e change mi iga ion, which equi es a global le el
o coo dina ion and coope a ion – we pe o med public goods and
common-pool esou ces games among Chinese and Spanish pa ici-
pan s. The ob ained esul s p o ide some insigh s on o he a iances
and uni e sali ies o people’s esponses in hese scena ios.
In his line, in ecen yea s, indi iduals and ins i u ions a e inc eas-
ingly conce ned wi h social and en i onmen al issues. Con ibu ions
in hese scena ios, none heless, equi es a subs an ial le el o al uism
by agen s who ha e o make cos ly decisions. We pe o med wo
expe imen s o unde s and he d i e s behind such decisions in wo
con empo a ily ele an si ua ions, namely, cha i y dona ions and so-
cially esponsible in es men s. Thei esul s indica e ha aming and
Figu e 6.7Nume ical esul s o he model. 116
Figu e 7.1Illus a ion o he model o memo y 1.122
Figu e 7.2
Coope a ion h i es a low mu a ion alues.
126
Figu e 7.3
F ac ion o coope a i e ac ions a he end o
each gene a ion. 127
Figu e 7.4
A e age coope a ion a he s a iona y s a e.
128
Figu e 7.5
Dis ibu ion o genes’ exp essed alues.
129
Figu e 7.6Eme ging S a egies. 132
Figu e 7.7
Coope a ion p obabili y in one-sho games.
133
Figu e 7.8
E olu ion o heu is ics wi h kin iden i ica ion
on LTT. 134
Figu e 7.9
E olu ion o heu is ics wi h kin iden i ica ion
on RRN. 135
Figu e 7.10
Coope a ion p obabili y in one-sho games o
he model wi h he kin iden i ica ion gene.
136
Figu e a.1
Chinese pa icipan s mani es ed s onge in-
di idualis ic p opensi ies han hei Spanish
coun e pa s. 155
Figu e a.2
Boo s apping con i ms he alidi y o he be-
ha io al eg ession model. 159
Figu e a.3
Pe o mance o he beha io al eg ession model
is s a is ically signi ican . 160
Figu e a.4
Beha io al eg ession model is obus o mis-
speci ica ion. 161
Figu e b.1
SD-be weenness de e mines payo s bu no
pos ed p ices. 164
Figu e b.2
Ex ension o Figu e 6.4o Chap e 6wi h he
50-nodes andom ne wo k. 165
Figu e b.3
E olu ion o cos s and p ices o each expe i-
men al ne wo k. 166
Figu e b.4Nume ical esul s o he model. 169
Figu e b.5Nume ical esul s o he model. 170
Figu e b.6
Nume ical esul s o he model o ne wo ks
wi h 50 and 100 nodes. 170
LIST OF TABLES
Table 2.1Decision heo y example 8
Table 2.2P isone s’ Dilemma payo s. 9
Table 4.1
Time-se ies analysis o he i ual o es ’s s a e.
58
Table 4.2Ta ge s in each session ype. 60
Table 4.3Homogeneous sessions eg ession. 63
Table 4.4He e ogeneous sessions eg ession 64
xii

lis o ables xiii
Table 5.1Numbe o pa icipan s in each coho 75
Table 5.2
Reg ession esul s o he con ibu ions o pub-
lic goods. 78
Table 5.3
Reg ession esul s o he dona ions o cha -
i y. 80
Table 5.4
Random E ec s eg ession wi h clus e obus
s anda d e o s a he indi idual le el o he
Fo ced Con ibu ion phase. 82
Table 5.5
Random E ec s eg ession wi h clus e obus
s anda d e o s a he indi idual le el o he
Keep in he Pocke phase. 83
Table 5.6Pa icipan s’ le el o educa ion 87
Table 5.7Coun y o Residence o pa icipan s. 88
Table 5.8P io Knowledge 89
Table 5.9Ques ions and F amings. 93
Table 5.10 F aming o ques ions. 94
Table 5.11
F aming o mul iple ques ions and und p o -
i abili y. 95
Table 5.12 Demog aphic a iables impac . 97
Table 6.1Expe imen al esul s. 109
Table 6.2
Nume ical esul s in expe imen al ne wo ks.
113
Table 6.3Nume ical esul s o la ge ne wo ks. 114
Table 7.1Memo y a iables and genes. 125
Table 7.2Pu e s a egies memo y. 130
Table 7.3
Classi ica ion o heu is ics acco ding o hei
esponses o he wo pu e s a egies. 130
Table b.1Expe imen al esul s. 163
Table b.2Coe icien s o he s a is ical models. 168
Table c.1
Dynamic panel model eg ession wi h clus-
e obus s anda d e o s a he indi idual
le el. 172
Pa I
PRELIMINARIES
1
INTRODUCTION
De ail om S one
Henge, Wil shi e,
eng a ed by Robe
Wallis, a e
J. M. W. Tu ne
We a e all app en ices in a c a whe e no one e e becomes a
mas e .
E ns Hemingway, New Yo k Jou nal-Ame ican
This hesis is conce ned wi h he beha iou o in e ac ing agen s.
They li e, ha e a no iceable cogni i e capaci y, and make decisions.
Speci ically, his hesis ocus on he mos in elligen and success ul li -
ing beings ha science knows so a : humans. Humans a e ecologically
dominan on he plane , ha ing sp ead o e di e se en i onmen s
like no o he species [1]. D i en by he s uggle o su i al in he
ha shness o he eal wo ld, humans conque ed he ea h by building
unique socie ies o un ela ed indi iduals [2], coope a ing in a scale
no i alled by any o he animal [3,4]. “To a la ge ex en
he u u e o he only
place whe e li e is
known o exis is
being de e mined by
he ac ions o
humans. Ye , he
powe ha humans
wield is unlike any
o he o ce o na u e,
because i is e lexi e
and he e o e can be
used, wi hd awn o
modi ied.”
Lewis and Maslin
[5]
Humans don’ ha e o wo y abou p eda o s anymo e, al hough
we a e o en wo ied abou ou sel es and ou ins i u ions. In his
ega d, con empo a y socie ies endu e challenges ha a e unique in
his o y. No because hey ha de o ha e wo se consequences, such a
s a emen canno escape he ealm o subjec i i y. Wha is clea is ha
con empo a y challenges a e a esul o , o a e in ensi ely a ec ed
by, he e e -changing An h opocene [5]. In less han 0.01% o he
ime o ea h’s exis ence, we ha e been able o al e he dynamics o
ecosys ems and e en he whole ea h clima e [6]. E en i we end up
ex inc , ou p esence and in luence on his plane will be a ailable
in he geological eco d o aeons [7]. A he ime o w i ing, socie y
is acing a global c isis as a pandemic p opaga es by he ae he o
connec ions we buil in he las cen u ies. E en he esilience o ou
socie y depends on how we in e ac wi h ou cons uc s and a e ac s,
as i is seen in he unce ain y associa ed wi h he e ec s o social
media in he o ms o go e nmen [8]. Wha e e we ha e o ace in
he u u e, we need o unde s and how humans beha e and how hey
espond o he o hcoming challenges. “We ha e c ea ed a
S a Wa s
ci iliza ion, wi h
S one Age emo ions,
medie al
ins i u ions, and
godlike echnology.”
Edwa d O. Wilson
[9]
In his ega d, i is c ucial o ha e in mind ha humans, al hough
unique in he animal kingdom [1,2], li e in g oups as o he social
animals and mani es beha iou which e ol ed bo h biologically and
cul u ally while hey in e ac ed wi h hemsel es [10]. This esul ed
in indi iduals ha some imes ha e o be s a egic bu can also beha e
sel lessly. Humans can sel ishly compe e o esou ces, bu also can
coope a e o each a common goal [11] and e en ac al uis ically in
a ou o o he s [12]. People ha e social p e e ences and migh choose
sub-op imal decisions o hem o he bene i o ano he , ye hey
3
4 in oduc ion
also ha e bias and p ejudices and show a ou i ism owa ds hei
own g oup [13,14]. Those beha iou s, mo eo e , can be in luenced by
en i onmen al and cul u al ac o s, by wha people see, hei cul u e,
and he s uc u es unde lying hei in e ac ions [15–18]. A guably,
hus, iden i ying people’s decisions while in e ac ing wi h o he s is
chie o examining con empo a y socie y’s cu en and imminen
a ai s.
In his hesis, we p esen ou wo k explo ing he beha iou o hu-
mans in scena ios o compe i ion, coope a ion, and al uism. These
in e ac ions ake place in games, a simple abs ac ion o s udy s a -
egy and con lic among in e ac ing agen s [19,20]. We obse e and
analyse hei beha iou h ough beha iou al expe imen s and also
explo e models based on obse ed beha iou as well on heo e ical
hypo heses. Ou goal is wo old, i s o in es iga e human beha iou
and inc ease ou collec ion o people’s esponses in s a egic games
and, second, o explo e bo h eme gence and implica ions o human
beha iou in heo e ical models. We begin in Chap e 2by p o iding
a b ie o e iew o he ounda ions o his hesis. As beha iou al
expe imen s a e essen ial o his hesis, in Chap e 3, we summa ise
he me hodology behind pe o ming hem. Subsequen ly, we p esen
ou wo k a anged in chap e s acco ding o hei con ex , namely:
collec i e ac ion p oblems In Chap e 4, we discuss wo
collec i e ac ion p oblems, namely public goods and common-pool
esou ces, among pa icipan s om wo coun ies. Sec ion 4.1p esen s
a social dilemma expe imen in which pa icipan s gain p o i by ha -
es ing a i ual o es ulne able o o e -exploi a ion. In Sec ion 4.2,
we explo e how in o ma ion and he dis ibu ion o a ge s in luence
a collec i e isk clima e-change dilemma game.You say you go a
eal solu ion
Well, you know
We’d all lo e o see
he plan
You ask me o a
con ibu ion
Well, you know
We’ e doing wha we
can
Re olu ion 1,
The Bea les
aming &al uism In Chap e 5, we p esen expe imen s
explo ing he in luence o aming and in o ma ion on dona ions
and esponsible in es men s. Sec ion 5.1p esen expe imen s using
mul iple public goods wi h an associa ed dona ion. In Sec ion 5.2, we
p esen one expe imen o unde s and he willingness o choosing
impac in es men op ions among expe s and non-expe s in his
ield.
ading in ne wo ks In Chap e 6, we p esen an expe imen
explo ing a gene aliza ion o he ba gaining game in complex ne -
wo ks. Fu he , we p opose a no el heo e ical model based on he
obse ed beha iou and discuss he esul s.
a heu is ic model o coope a ion In Chap e 7, we expose a
heo e ical wo k a emp ing o answe he p oblems unde lying coop-
e a ion in humans by using an o iginal model o heu is ics selec ion.

in oduc ion 5
Finally, we conclude in Chap e 8by summa ising he indings o
his hesis and exposing some p ospec i e ema ks. Necessa y esul s
ha we deemed no su icien ly ele an o he main ex a e discussed
in he Appendices 1.
1
De ails o each expe imen al session we e omi ed o compac ness, such as socio-
demog aphic cha ac e is ics, ins uc ions and e hical s a emen s. They can be ound
in he supplemen a y ma e ials o he co esponding publica ions.
2
FOUNDATIONS
Cedalion s anding on
he shoulde s o
O ion om Blind
O ion Sea ching
o he Rising Sun
by Nicolas
Poussin.
Le Pascal say ha man is a hinking eed. He is w ong; man is a
hinking e a um. Each pe iod in li e is a new edi ion ha co ec s
he p eceding one and ha in u n will be co ec ed by he nex ,
un il publica ion o he de ini i e edi ion, which he publishe
dona es o he wo ms.
Machado de Assis, The Pos humous Memoi s o B ás Cubas
In his chap e , we p esen he heo ies and esul s o ming he basis
o his hesis. The eade migh no ice ha he desc ip ions a e b ie
and cen e a ound he opics which a e mos ela ed o ou wo k, as
hese ields ha e a my iad o b anches, and a ho ough desc ip ion
would be ou o scope. Ne e heless, hey a e su icien o a p ope
comp ehension o he nex chap e s. We begin by p esen ing he
app oaches by ma hema icians in he ields o decision heo y and
game heo y in Sec ion 2.1. Subsequen ly, we de ail esul s ob ained
in he ield o expe imen al economics conce ning human beha iou
in games 2.2, and Sec ion 2.4 hen desc ibes some o he heo ies
explaining he obse ed beha iou . As some o hese indings and
e en ou own o expe imen al wo k (Chap e s 6and 7) equi es a basic
unde s anding o ne wo ks, we b ie ly in oduce some o i s heo y in
Sec ion 2.3. Finally, we conclude in Sec ion 2.5.
2.1 heo ies on decisions and games
Pensées
(“Though s”) by
Blaise Pascal.
In he 17 h-cen u y, Blaise Pascal published he Pensées, a collec ion
o ex s including he amous Pascal’s Wage whe ein he p o ides an
a gumen in a ou o heism. In i , Pascal conside s ha humans be
hei li es on he exis ence o God. I God exis s, a ue belie e should
ecei e an in ini e bene i : sal a ion o e e ni y. Con e sely, a non-
belie e would be doomed o e e ni y, an in ini e punishmen . I God
does no exis , on he o he hand, as humans li e a ini e li e, humans
can only ecei e a ini e bene i , li ing wi hou he cons ain s imposed
by eligion, o a ini e loss, was ing hei li es wi h he belie e cho es.
Thus, humans a e gamble s wi hou he knowledge o God’s exis ence
and obliged o be in one op ion du ing hei li e ime. His a gumen
ollows a p obabilis ic easoning, by weighing expec ed alue o each
consequence he only a ional choice would be o be ha God exis s
and li e acco dingly1.
1
This, o cou se, does no conside he p oblem o choosing he igh dei y o belie e
in, and o knowing wha I would wan om i s belie e s.
7
8 ounda ions
-i ains i does no ain
Take he umb ella -1-1
Lea e he umb ella a
home
-10 0
Table 2.1:Decision heo y example.
Illus a ion o u ili y alues when de-
ciding o ake o no ake he umb ella when going ou .
Pascal’s essay p obably cons i u es he i s ex on decision heo y [20,
21], which s udies how agen s make decisions. I posi s ha agen s
ha e belie s and desi es and ac a ionally acco ding o hem. Mo e
speci ically, hei p e e ences de e mine a co esponding u ili y ha
will be maximized by a ional decision-make s, i.e., hey will consis-
en ly choose he op ion wi h he maximum expec ed u ili y alue.
When deciding in ol es unce ain y, i is o en assumed ha agen s
ha e a subjec i e p obabili y dis ibu ion conce ning he unknowns. As
an illus a ion, imagine one pe son has o decide i she akes he um-
b ella wi h he when going ou , ca ying i implies a cos , al hough
smalle han he cos o no ha ing an umb ella i i ains. The u il-
i ies associa ed wi h each ou come in his example a e desc ibed in
Table 2.1. Agen ’s decision will depend on hei belie s abou he
aining p obabili y – e.g., i he e is 0.5chance o aining, a a ional
decision-make should ake he umb ella wi h he .
Decision heo y eaches i s bounda ies when agen s a e in e ac ing
wi h o he s, and hei decisions depend on he ac ions o o he a ional
indi iduals. In hese cases, he subjec i e p obabili y dis ibu ion o
one agen will depend on he decision-making p ocess o he o he s i
is in e ac ing wi h, and ice- e sa. In o he wo ds, he subjec i e p ob-
abili y dis ibu ion o one a ional agen is an inpu o he dis ibu ions
o all he o he s, leading hus o a sys em o equa ions. To sol e such
sys ems eme ged he ield o game heo y, acco ding o Roge Mye son,
he essen ial logical ul ilmen o decision heo y [20].
In game heo y, he wo d games e e s o any si ua ion o s a egic
in e ac ion be ween sel -in e es ed pa s. They a e elemen a y compo-
nen s o social g oups, as pu by Colin Came e : “a ough equi alen
o social science o he pe iodic able o elemen s in chemis y” [15].
Games a e abs ac si ua ions whe ein in ol ed agen s, o playe s,
ob ain a bene i acco ding o he combina ion o hei ac ions; de-
spi e hei simplici y, hey p o ide a powe ul amewo k o s udy
eal-wo ld in e ac ions. Game heo y conside s a ional and in elli-
gen playe s, he la e cha ac e is ic meaning ha hey can ind he
op imum decision i such exis s [20]. Thus, i he e is a ma hema -
ical solu ion o he decision-making p oblem, i will co espond o
he agen decision. Commonly, s udies ocus on wha is known as
non-coope a i e game heo y, which deals speci ically wi h he game
2.2 human beha iou in expe imen s 15
P opose s should o e he minimum amoun possible (e.g., 1cen ),
while he Responde s should accep any posi i e o e . Expe imen s,
none heless, show ha P opose s a e willing o sha e signi ican ly
mo e han he minimum, wi h amoun s usually being g ea e han
Dic a o s’ o e s [15]. This shows ha , as P opose s a e conce ned wi h
Responde s ejec ing hei o e , hey end o p opose highe alues
han Dic a o s. The e o e, hese esul s p o ide a clea indica ion o
he wo essen ial ea u es o people: being bo h s a egic and al uis ic.
Impo an ly, people’s beha iou is a ec ed by he speci ics o he si -
ua ions in which hey a e in e ac ing. Besides, no e e ybody beha es
equal [40] and changing he game s uc u e and cul u e o he pa -
icipan s deeply a ec game ou comes [15]. Expe imen al economics
p o ides, he e o e, one powe ul pa adigm o u he unco e how
people beha e and why hey beha e as hey do. As no ed by Colin
Came e , “ he goal is no o disp o e game heo y bu o imp o e i , by es ab-
lishing egula i y, which inspi es new heo y” [15]. Knowledge ob ained
empi ically can be used hen o c ea e new heo ies, which can be
u he es ed by new expe imen s. This has been he case in ou wo k
p esen ed in his hesis, such as desc ibed in Chap e s 4and Chap e
6.
In he ollowing subsec ion we will b ie ly in oduce he me hodol-
ogy behind expe imen ing in economics and illus a i e expe imen al
esul s o he Public Goods Game, as i ela es he mos o he wo k
p esen ed in his hesis 4.
2.2.1The me hodology o expe imen s
Al in Ro h [43] ca ego ize economic expe imen s acco ding o hei
goals in h ee ypes: i) Speaking o heo is s: expe imen s wi h he goal
o es ing hypo hesis o igina ed om heo y; ii) Sea ching o ac s: ex-
pe imen s looking o new phenomena in se ings wi h some modi ied
si ua ion; iii) Whispe ing in he ea s o p inces: expe imen s planned
o policymaking. Ini ially expe imen al economics was mos ly con-
ce ned wi h es ing economic heo y p edic ions, nowadays, howe e ,
i mos ly conce ns wi h es ing how a ia ions in he expe imen al
se up can in luence ou comes. This implies ha expe imen s can lack
an unde lying igo ous heo y and can be used o es in o mal hy-
po hesis [30]; in o he wo ds, hey would be sea ching o ac s (ii).
No ably, ou expe imen s epo ed in his hesis all on his ca ego y.
Speci ically, ou expe imen s can be di ided in o wo ypes: looking
o di e ences in beha iou be ween di e en popula ions (Chap e
4); o looking o di e ences be ween wo expe imen al ea men s in
he same popula ion (Chap e s 5and 6).
4See [15,41,42] o a b oad o e iew o expe imen al economics esul s.

16 ounda ions
2.2.1.1The limi a ions o expe imen s
Expe imen e s a e o en looking o phenomena ha can be cha ac-
e ized quali a i ely, as p ecise quan i a i e p edic ions a e i ually
impossible o be ob ained [30]. Expe imen al condi ions can ha e
p o ound e ec s on he inal esul , being gene ally un easible o
ep oduce p ecisely da a om p e ious expe imen s. This o ces ex-
pe imen e s when es ing a hypo hesis o ep oduce p e ious esul s
o some ex en ; o he wise, i would no be easible o dis inguish
he causes behind he obse a ions. Speci ically, esul s will depend
on he speci ic con ex o each execu ion: i s ini ial condi ions (e.g.,
socio-demog aphic cha ac e is ics o he popula ion), and he auxil-
ia y assump ions abou he expe imen s (e.g, he pa icipan s ha e
unde s ood he ins uc ions). The e o e, an expe imen al conclusion
ob ained by e idence
e
, which suppo s o e u es a hypo hesis
H
, is
also de e mined by he ini ial condi ions
I
and auxilia y assump ions
K:
(K∧I∧H) =⇒e(2.9)
This implies ha i is no only impossible o p o e he gene al u h
5
o a hypo hesis when
e
is obse ed, bu also o e u e i in a deduc i e
app oach when
e
is no obse ed. This is known as he Duhem-Quine
p oblem, and i has di ec implica ions when d i ing conclusions om
expe imen al esul s. The con olled expe imen enables he es ing
o hypo hesis, bu by being con olled i is a om he messiness
o eal-wo ld in e ac ions; hypo heses a e no con i med in isola ion.
The e o e, in e ences ha e o be made wi h ca e when ex apola ing
expe imen al esul s. They a e a aluable sou ce o insigh s, bu only
can ake us so a , as Guala pu s i : “da a – no ma e how use ul – canno
ul ima ely eplace he e idence collec ed in he ield” [45].
2.2.1.2The case o Public Goods
“Public goods and
dilemma expe imen s
a e like using
ping-pong balls;
sensi i e enough o
be eally in o ma i e
bu only wi h
adequa e con ol.”,
John Ledya d [46]
The Public Goods Game p o ides a good case s udy o how knowledge
abou human beha iou is ob ained in he lab. Aside om being one
o he mos pa adigma ic expe imen s in economics, i is connec ed
o he majo i y o wo ks p esen ed in his hesis. Resul s om ea ly
expe imen s ha e shown ha indi iduals would no ee ide; hey
would con ibu e some hing o he public good. Gene ally, pa ici-
pan s would be willing o con ibu e some hing be ween 40% and
60% o hei endowmen [46]. None heless, i expe imen e s allowed
he game o un epea edly o some pe iods, con ibu ions would
e en ually decay owa ds he Nash equilib ium [48]. This phenomena
has some imes been e e ed o as he o e con ibu ion and decay and
5
Acco ding o he deduc i is iew [30,44], we ne e can con i m ha
H
is ue, only
ha i is alse. Consequen ly, science would e ol e by disp o ing alse heo ies.
2.2 human beha iou in expe imen s 17
Figu e 2.1:Expe imen al esul s o a epea ed Public Goods Game, wi h
and wi hou punishmen .
Each panel shows mean coope a ion
a each ime pe iod. Top panel (
a
) shows sessions whe ein pa ici-
pan s s a ed in he punishmen ea men and he bo om panel
(b) in a ea men wi hou punishmen . Figu e om [47].
has been in ensi ely eplica ed [30]. On one hand, he posi i e con i-
bu ion shows again ha humans end o ac p o-socially, on he o he
hand, he decay also demons a es ha his is no an uncondi ional
endency.
One explana ion o he decay phenomena is he impossibili y o
di ec e alia ion by pa icipan s, as wi hd awing con ibu ions will
also impac non- ee- ide s. In his line, an expe imen by Feh and
Gach e allowed pa icipan s o punish o he s a e he con ibu ion
phase [47]. To assess he e ec o punishmen , hey had o pe o m wo
ea men s: one wi h, and one wi hou punishmen ; he equi emen o
a con olled expe imen . They obse ed signi ican di e ences be ween
he wo ea men s: con ibu ions we e highe , and he decay was no
obse ed when pa icipan s could punish, as shown in Fig. 2.1. This
phenomena was connec ed wi h a new hypo hesis conce ning human
p o-sociali y [47,49,50], as we commen in Sec ion 2.4. None heless,
hese esul s ha e o emain cons ained o a na ow labo a o y scope
un il e idence is ob ained in he ield [45].
18 ounda ions
2.3 s uc u e: he sine qua non o in e ac ions
The Se en B idges
o Königsbe g
I we a e o s udy in e ac ions, we a e obliged o unde s and he
s uc u e unde lying hem. One use ul app oach is o ep esen he
in e ac ing en i ies as e ices (nodes) o a g aph (o ne wo k) and ep-
esen hei connec ions as i s edges (links), being his ep esen a ion
c ucial o some o ou wo k (Chap e s 6and 7). G aph heo y is a
b anch o ma hema ics conside ed o ha e begun wi h he wo k on
he se en b idges o he P ussian ci y o Königsbe g by he ma he-
ma ician Leonha d Eule . In i , Eule mapped i e islands and he
b idges be ween hem as he e ices and he edges o a g aph, e-
spec i ely. This ep esen a ion allowed him o show ha he e was
no pa h, mo e speci ically no Eule ian pa h, ha could isi each node
(island) wi hou isi ing an edged (c ossing a b idge) wice in he
Königsbe g b idges’ g aph. Recen ly, his app oach o modelling eal
sys ems as g aphs ha e con e ged o he ield o ne wo k science [51,
52], commonly e e ing o hem as ne wo ks.
a
b
c
d
A g aph is usually
ep esen ed by
ha ing i s nodes as
ci cles and edges as
lines.
In he social sciences, he i s known use o ne wo ks o ep esen
in e ac ions be ween indi iduals is o en a ibu ed o he school map-
ping by Jacob Mo eno [53], whe ein he mapped in e ac ions be ween
boys and gi ls s uden s in a sociog am. Wi h his ep esen a ion, ocus
on indi iduals was supplan ed by a new holis ic pe spec i e: nodes as
in e dependen uni s connec ed by edges ep esen ing channels o he
low o esou ces, oppo uni ies/cons ain s o in e ac ions, o las ing
ela ion be ween indi iduals [54]. This change in pe spec i e gained
mo e momen um in he 20 h cen u y as da a om social and economic
in e ac ions [55] became a ailable. Concu en ly, di e en ields began
o s udy he s uc u e in e ac ions o di e se ype o sys ems, such as
he wo ld wide web [56], powe g ids [57], and p o ein ne wo ks [58].
Rema kably, p ope ies om di e en ypes o sys ems could be
explained by abs ac and gene ic models [59,60], indica ing ha
he unde lying s uc u e migh ha e deep e ec s in he esul ing
phenomena, which is also he case o he sys ems s udied he e. Thus,
we will in oduce basic de ini ions om g aph heo y and he ne wo k
models equi ed o he unde s anding o ou esul s 6.
2.3.1G aphs & Ne wo ks: De ini ions and P ope ies
A g aph
G= (V,E)
is a s uc u e composed o
|V|>0
e ices
(nodes) connec ed acco ding o he se
E={e1,e2, . . . }
o edges (links).
Commonly, g aphs a e ep esen ed by an
|V|x|V|
adjacency ma ix
A
whe ein each cell
Ai,j=1
i he e is an edge be ween e ex
i
and
j
,
and
Ai,j=0
o he wise. Mo eo e , i he edges ha e di ec ionali y –
6
Fo a gene al in oduc ion on ne wo ks, see [61–63]. Mo eo e , [64] p o ides a
summa y o basic models p ope ies, [54] gi es an in oduc ion o social ne wo ks,
and [55] p o ides an in oduc ion o he s udy o economic ne wo ks.
2.3 s uc u e: he sine qua non o in e ac ions 19
i.e., hey a e o de ed pai s –
G
is denomina ed a di ec ed g aph, and
an undi ec ed g aph o he wise. Each e ex has an associa ed deg ee
k
,
which co esponds o he numbe o edges i belongs o:
k =∑
j∈VA ,j(2.10)
I
G
is di ec ed, he deg ee can be decomposed in o he in-deg ee
(
kin
), edges a i ing a
; and he ou -deg ee (
kou
), edges ou going
om :
kin
=∑
j∈VA ,j(2.11)kou
=∑
j∈VAj, (2.12)
The a e age deg ee
hki
o a ne wo k is o en used o cha ac e ize
i . Mo eo e , di e en g aph gene a ing p ocesses a e expec ed o
gene a e di e en deg ee dis ibu ions, i.e., a dis ibu ion such ha
P(k)
co esponds o he p obabili y o a andomly chosen e ex
ha ing deg ee
k
. Consequen ly, he empi ical deg ee dis ibu ion o en
p o ides subs an ial in o ma ion abou he unde lying mechanisms o
he connec ions in a eal ne wo k.
2.3.1.1Pa hs
Ne wo ks o en ep esen s uc u es o a e sal, as occu wi h ans-
po a ion [65–68] and compu e ne wo ks [69–71]. In o he ypes o
sys ems, dis ances be ween nodes migh be also impo an as hey can
indica e he s eng h be ween he indi ec ly connec ed en i ies. In his
ega d, ne wo ks’ pa hs a e one o hei mos use ul a ibu es. A pa h
co esponds o a sequence o dis inc e ices such ha each consecu-
i e e ex pai co esponds o an edge in he g aph. A simila ype
o sequence, wi hou he e ex dis inc i eness es ic ion, is called a
walk and can consequen ly be in ini e. The leng h o a pa h is gi en
by he numbe o edges i a e ses, namely, i s numbe o e ices
−1
. Mos impo an ly, he dis ance (
d
) be ween wo e ices is gi en
by he minimum pa h leng h be ween hem, which co espond o he
leng h o he sho es pa h o he geodesic be ween hem. Conce ning
he whole ne wo k, one in o ma i e me ic is i s a e age pa h leng h
hdi
, which co esponds o he a e age geodesic be ween all e ices
pai s:
hdi=∑V
u6= d(u, )
|V|(|V|−1)(2.13)
2.3.1.2Cen ali ies
One o he ecu en ques ions while s udying ne wo ks conce ns he
indi idual impo ance o i s e ices. Ce ain nodes can be c i ical o
some p ocess [72], and usually his can be seen by hei posi ion in
he g aph, i.e., by how cen al i is. Di e en me ics ha e eme ged o
20 ounda ions
measu e e ices cen ali ies acco ding o he speci ic con ex , as he
analysis desc ibed in Chap e 6. The mos s aigh o wa d cen ali y
me ic co esponds o he e ices’ deg ee, despi e simple i can ne -
e heless be e y powe ul, as he numbe o connec ions o a node
is likely o be e y in o ma i e o i s ole in he sys em. Some o he
commonly used cen ali ies me ics ele an o ou wo k a e 7:
be weenness Be weenness cen ali y
b
measu es how impo an
a e ex
is, wi h espec o he possible pa hs be ween pai o nodes.
Namely, i measu es, he ela i e numbe o sho es pa hs a e ex
belongs o:
b( ) = |V|
∑
6=s6=d
σs,d( )
σs,d(2.14)
This summa ion akes place o all pai o nodes wi hou
, whe ein
σs,d( )
s ands o he numbe o sho es pa hs be ween e ices
s
and
d
con aining
, and
σs,d
o he o al numbe o sho es pa hs be ween
sand d.
closeness Closeness cen ali y
C
measu es how close a e ex
is o all he o he e ices. Speci ically, i co esponds o he a e age
dis ance o all he e ices o he g aph, hus, a low alue should
indica e a mo e cen al e ex. I is gi en by:
C( ) = ∑u∈Vd(u, )
n(2.15)
2.3.1.3Clus e ing
I e ice
a
is connec ed o e ice
b
, and
b
is connec ed o e ice
c
,
how likely is o
a
and
c
o be connec ed? In p obabilis ic e ms, he
answe would be always 1i all he connec ions we e ansi i e, which
would only occu in a comple e g aph. This is ex emely unlikely o
be he case in eal ne wo ks, al hough hey o en exhibi some pa ial
ansi i eness. T ansi i i y can be measu ed by aking in o accoun he
ac ion o imes he ela ion (a,b)&(b,c) =⇒(a,c), i.e., he numbe
o imes he exis ence o a pa h o leng h 2implies a loop o leng h
3. Commonly, his will be done by calcula ing he g aph’s clus e ing
coe icien (
CC
), which co esponds o he numbe o closed iangles
(3- e ices clique) o e e y pa h o leng h wo, o iple:
A loop o leng h 3o
a3- e ices clique. CC(G) = 3|4(G)|
|τ(G)|(2.16)
Whe ein
4(G)
co esponds o he se o all closed iangles in
G
and τ(G) o he se o all iples in G.
7Fo a b oade lis o me ics, see:[63, Chap e 7]

2.3 s uc u e: he sine qua non o in e ac ions 21
2.3.2G aph models
In his subsec ion, we in oduce some ma hema ical models used o
gene a e g aphs. He e he eade migh obse e ha one essen ial
cha ac e is ic dis inguishing g aph models is hei expec ed deg ee
dis ibu ion o deg ee sequence.
2.3.2.1E d˝os–Rényi G aph
The E d˝os–Rényi andom g aph, usually e e ed o as ER g aph,
was in oduced by ma hema icians Paul E d˝os and Al éd Rényi. In
he ER model, a g aph
G(n,p)
has
n
e ices connec ed andomly o
each o he wi h a p obabili y
p
. As each edge occu s independen ly
om e e y o he ,
G
is expec ed o ha e
(n
2)p
edges and i s deg ee
dis ibu ion is gi en by a binomial dis ibu ion o he o m:
P(k) = n−1
kpk(1−p)n−1−k(2.17)
Whe ein
P(k)
co esponds o he p obabili y o a node ha ing de-
g ee
k
. Fo la ge
n
, he dis ibu ion can be app oxima ed by a Poisson
dis ibu ion:
P(k) = ehkihkik
k!(2.18)
As he p obabili y o wo e ices being connec ed is he same o
e e y pai o e ices, a closed iple will be connec ed wi h p obabili y
p. In o he wo ds, he p obabili y o being connec ed is gi en by:
CC(G) = hki
n−1(2.19)
This implies ha o la ge ne wo ks, he clus e ing coe icien ends
o anish. Real ne wo ks, none heless, end o ha e a ela i ely la ge
clus e ing coe icien , he eby demons a ing ha connec ions do no
occu andomly. On he o he hand, he a e age pa h leng h in an
ER g aph ends o ela i ely small, such as is encoun e ed in eal
ne wo ks:
hdi ∼ lnn
lnhki(2.20)
2.3.2.2Small-Wo ld Ne wo ks
In 1967, S anley Milg am published he esul o a se ies o expe imen s
in he social sciences, whe ein pa icipan s we e gi en an unknown
ecipien ha should ecei e a le e sen by hem [73]. As he a ge
was a comple e s ange , hey we e ins uc ed o send he le e o
one pe son hey knew in he i s name basis who should o wa d he
le e ollowing he same me hod. Rema kably, le e s ha eached
22 ounda ions
Figu e 2.2:T ansi ion om a ing la ice o a andom g aph.
Fo small al-
ues o
p
, a small-wo ld egime exis s, in which g aphs will ha e
a small a e age pa h leng h and a la ge clus e ing coe icien .
Figu e om [59].
he ecipien had only been o wa ded 6 imes on a e age. F om his
esul eme ged he no ion o he “6deg ees o sepa a ion”, in ha we
a e only a e 6s eps away om e e y o he pe son in he wo ld; hus,
we li e in a small wo ld.
One compelling explana ion o his phenomenon was published
in 1998 by Duncan Wa s and S e en S oga z in one o he mos
in luen ial pape s in ne wo k science [59]. Thei model s a s om a
egula ing la ice, in which e e y node is connec ed wi h hei
hki
nea es neighbou s, such as illus a ed in he le g aph o Fig. 2.2.
I s edges a e ewi ed acco ding o a p obabili y
p
, inc emen ing he
diso de o he sys em as
p
g ows. Thus, when
p=1
a andom g aph
is ob ained, such as he igh g aph o Fig. 2.2. In e es ingly, o small
p>0
, he esul ing g aph has a small a e age pa h leng h, compa able
wi h a andom g aph, bu wi h a la ge clus e ing coe icien , as shown
by he g ey a ea o Fig. 2.3. This is a esul o ewi ing adding sho cu s
o he g aph, while he g aph con inues o be highly clus e ed as
p
is
small, as illus a ed by he middle g aph o Fig. 2.2.
2.3.2.3Ba abasi-Albe
One impo an cha ac e is ic o eal ne wo ks, no ully de eloped
by he p e ious models, is hei high deg ee he e ogenei y. In eal
ne wo ks, some nodes can ha e signi ican ly mo e connec ions han
o he s, an unlikely esul o a andom p ocess. Speci ically, i has been
obse ed ha he deg ee dis ibu ion o some ne wo ks ollows a
powe -law dis ibu ion [56,60,74,75] o he o m
P(k)∼k−γ
, such
ha ypically
2≤γ≤3
[63]. In e es ingly, his ype o dis ibu ion
is scale-in a ian , leading o such ne wo k being e e eed as scale- ee
ne wo ks.
The p e e en ial a achmen p ocess is he mos well-known expla-
na ion o such dis ibu ion [60]. I co esponds o a eedback-loop
be ween connec ions, whe ein nodes wi h high connec i i y a e mo e
2.3 s uc u e: he sine qua non o in e ac ions 23
0.00
0.25
0.50
0.75
1.00
10−5 10−4 10−3 10−2 10−1 100
p
Figu e 2.3:A e age pa h leng h and clus e ing coe icien in Wa s-
S oga z ne wo ks.
No malized a e age pa h leng h (solid black
ci cles) and clus e ing coe icien (open ci cles). Values co espond
o a mean o 102o 103nodes ne wo ks.
likely o ob ain new connec ions. This p oposal was i s ly posi ed by
“I is common in
bibliome ic ma e s
and in many di e se
social phenomena,
ha success seems o
b eed success.”
De ek de Solla
P ice [76]
P ice in 1976 [76] by he name o cumula i e ad an age, explaining how
highly ci ed esea ch pape s a e mo e likely o be ci ed. None heless,
he wo k by Lazlo Ba abasi and Reka Albe in 1999 [60] became he
mos amous using his app oach. In hei model, hey conside a
g owing ne wo k, in which a node a i es wi h
m
new edges a each
ime s ep. I will connec hose
m
edges o exis ing nodes in p opo ion
o hei deg ees, a p e e en ial a achmen p ocess, as coined by hem.
This will gene a e a ne wo k wi h a deg ee dis ibu ion ollowing
exac ly P(k)∼k−3, as lus a ed by Fig. 2.4.
2.3.2.4Con igu a ion Model
The con igu a ion model was p oposed by Béla Bollobás [77] o s udy
g aphs ha ha e a deg ee sequence ixed be o ehand. This allows
speci ying ha e e y node has deg ee g ea e han ze o, which is no
possible wi h he ER g aph. Mo eo e , i enables he speci ica ion o
any deg ee sequence, being also use ul o gene a ing g aphs wi h a
powe -law deg ee dis ibu ion wi hou co ela ed deg ees [78]. Gi en
a ixed deg ee sequence (
k1,k2,··· ,kn
), i gene a es a g aph acco ding
o he ollowing algo i hm:
1.
Gene a e
∑n
iki
hal -edges, whe ein o each e ice
i
he e is
ki
hal edges connec ing o i ;
2.
Randomly connec s he pai s o hal -edges o o m an edge o
he g aph.
Clea ly,
∑n
iki
has o be e en as
∑n
iki=2|E|
. This p ocedu e does
no gua an ee ha gene a ion o a simple g aph, as sel -loops and
24 ounda ions
10−6
10−5
10−4
10−3
10−2
10−1
100
100101102103104105106
k
P(k)
Figu e 2.4:Deg ee dis ibu ion in a scale- ee ne wo k.
Deg ee dis ibu ion
o a ne wo k wi h
106
nodes gene a ed by he Ba abasi-Albe
model, o
m=5
[60]. The dashed line co esponds o a line wi h
slope 3 o guide he eye.
mul iple edges a e possible. Ne e heless, bo h end o ela i ely wane
when
n→∞
[64]. Fo he gene a ion o ne wo ks ollowing a powe -
law deg ee dis ibu ion i has been shown ha , i he maximum deg ee
is smalle han he squa e oo o i s size (
kmax ≤√n
), nodes’ deg ee
will no be co ela ed [78].
andom egula ne wo k Also known as a uni o m andom
egula g aph, i is a subse o he k- egula g aphs, i.e, g aphs whe ein
all nodes ha e he same deg ee
k
. I co esponds o a andom g aph
gene a ed by he con igu a ion model by se ing a ixed deg ee o
k
o e e y node.
2.4 explaining coope a ion
P e ious sec ions ha e demons a ed ha he ini ial p edic ions o
game heo y poo ly p edic ed he beha iou o humans. People coop-
e a ed in expe imen s in which hey should de ec , hey sha ed and
dona ed money expec ing no bene i om i . Indeed, humans coop-
e a e in a unique scale, li ing in socie ies whe ein us and suppo
among un ela ed indi iduals a e impe a i e [2]. Mo eo e , coope a-
ion is also obse ed in he whole na u e, om bac e ias and cells o
p ima es and o he mammals [79]. This posed a challenge o e olu-
iona y biology, as a i s glance cos ly beha iou in a ou o o he
indi iduals should no be selec ed [80]. As i u ns ou , coope a i e
beha iou can p o ide i ness ad an ages in ce ain condi ions. In his
sec ion, we p o ide a b ie desc ip ion o he main explana ions o he
biological e olu ion o coope a ion and in which condi ions humans
end o coope a e.
3
PERFORMING EXPERIMENTS
“The e a e wo possible ou comes: i he esul con i ms he
hypo hesis, hen you’ e made a measu emen . I he esul is
con a y o he hypo hesis, hen you’ e made a disco e y.”
En ico Fe mi
Pla e 1,3 om
Cha les Ba gue’s
Cou s de dessin
Beha iou al expe imen s do no equi e a la ge appa a us o be
pe o med, good esea ch can be done wi h pencil and pape [127,128]
o e en wi h a bowl o beans [129]. None heless, unless he speci ics o
he expe imen equi e o he wise, i is p e e ed o un he expe imen
using a compu e pla o m. In his way, session e ec s [130] due o
expe imen e in luence and human mis akes a e educed. Mo eo e ,
non-compu e ized expe imen s a e signi ican ly mo e ime consuming,
especially i pa icipan s a e playing in g oups. Fo ins ance, in a
epea ed public goods game a he end o e e y ound, he g oups’
o al con ibu ion and pa icipan s’ payo ha e o be calcula ed, which
would be o e whelming i pa icipan s a e no playing o e a compu e
ne wo k.
Fo he a o emen ioned easons, all he expe imen s epo ed in
he nex chap e s ha e been pe o med using a so wa e pla o m.
Speci ically, excep ing expe imen s epo ed in Sec ions 5.1
1
and 6.1
2
,
all he expe imen s epo ed ha e been de eloped and pe o med by
he au ho .
3.1 planning
The i s s age o an expe imen usually is elabo a ing he ideas behind
i , consolida ing hem in a p ac ical se up. Wha scena io is in ended
o be ep oduced o emula ed in he lab? Wha hypo heses a e going
o be es ed? Wha beha iou do we wan o obse e? A e ha has
been decided, i is necessa y o ou line wha a e he equi emen s in
e ms o so wa e and da a. The o me will de e mine how elabo a ed
he sys em will ha e o be, and he la e how many pa icipan s and
g oups will be needed o ha e enough s a is ical powe . Subsequen ly,
i is necessa y o p epa e he ins uc ions o he subjec s explaining
he expe imen and s a he so wa e de elopmen p ocess. Ideally,
he p ojec s a s wi h a equi emen analysis ollowed by he design o
he so wa e gua an eeing a clea s uc u e and he possible eusabili y
o he p og am [131].
1I has been de eloped by he LINEX ins i u e in Valencia.
2I has been de eloped by he so wa e de elope s a he BIFI Ins i u e.
31

32 pe o ming expe imen s
3.2 de eloping
The so wa e o pe o ming an expe imen has se e al equi emen s:
i needs a clea in e ace wi h unde s andable ins uc ions; i has
o manage g oups o playe s playing simul aneously, synch onizing
ounds h ough wai ing pages; pa icipan s inpu s ha e o be s o ed in
a cen al da abase. This migh seem a he daun ing, o ui ously, how-
e e , eusabili y is sp ead in so wa e de elopmen . The a ailabili y o
code om people ha con on ed simila p oblems emo es he bu -
den o ein en ing he wheel in e e y en e p ise. In ou case, almos
all o ou expe imen s we e based on he oT ee pla o m [132], which
i sel depends on se e al o he ee so wa e, such as Django
3
, Boo -
s ap
4
and Redis
5
. In oT ee, an expe imen is s uc u ed acco ding o
he ollowing nes ed componen s6:
Session:
s uc u e co esponding o he expe imen al session, i
is di ided in o a lis o subsessions.
Pa icipan :
en i y co esponding o he pa icipan play-
ing he expe imen , hus i e e ences all he ac ions pe -
o med by he in he inne classes.
Subsession:
he elemen a y cons i uen o each session,
usually i co esponds o one ound in he game. None he-
less, one ound also migh be ac ioned in o mo e subses-
sions.
G oup:
s uc u e con aining a se o playe s, o in-
s ance, in public goods games each g oup o playe s
wi h access o a common und would be con ained in a
sepa a e g oup.
Playe :
s o es he ins ance o play by he pa ici-
pan in one pa icula subsession. Thus, i allows
o a pa icipan o ha e di e en playe oles in
each subsession. Fo ins ance, in subsession A, he
playe can be he P opose in an Ul ima um game,
while in subsession Bshe will be he Responde .
Page:
he elemen a y di ision o a subsession,
each page is isi ed by a playe and cons i u es
one s ep o he expe imen .
The e o e, gi en ha he co e o he so wa e equi emen s is al-
eady aken ca e o by oT ee, mos o he de elopmen consis s in
3h ps://www.djangop ojec .com/
4h ps://ge boo s ap.com/
5h ps:// edis.io/
6
Mo e de ails on how o de elop an expe imen wi h oT ee a e a ailable a
h ps:
//o ee. ead hedocs.io/en/la es /index.h ml
3.2 de eloping 33
de eloping he speci ics o he expe imen : da a modelling, con igu a-
ion and layou o he pages, any calculus pe o med a each ime s ep,
con ol o pa icipan s sequence o play, ansla ions (in he case o
mul ilingual expe imen s), e c. Hence, mos o he e o is gene ally
spen wi h he expe imen al in e ace, which none heless can be e y
ime-consuming. Fo ins ance, he o es ep esen a ion displayed in
he expe imen p esen ed in Sec ion 4.1 equi ed he de elopmen
o a lib a y o con ol he map d awing and he esou ce s a es. The
ins uc ions also ha e o been de eloped ca e ully, i should s a e in
clea and simple sen ences wha he expe imen is abou and p o ide
a u o ial on how o play he game. As an illus a ion, we display
below he ins uc ions o he expe imen p esen ed in Chap e 6.
34 pe o ming expe imen s
Ins uc ions
Thank you o pa icipa ing in his expe imen , ha
is pa o a esea ch p ojec in which we y o
unde s and how indi iduals make decisions. You e
no expec ed o beha e in any pa icula way. A his
momen he expe imen begins. Please keep quie un il
he end, u n you cell phone o , and emembe ha
he use o any ma e ial o eign o he expe imen is
no allowed (including pen, pencil o pape ).
You ea nings will depend on you own decisions and
hose o he o he pa icipan s. Addi ionally, you will
ecei e 5 e o pa icipa ing in he expe imen un il
he end.
Please keep quie du ing he expe imen . I you need
help, aise you hand and wai o be assis ed. Please
do no ask any ques ion aloud.
You pa icipa e along wi h o he people wi h whom you
in e ac acco ding o he ules explained below. The
session las s abou an hou and a hal . The ollowing
ins uc ions a e he same o e e y pa icipan o his
expe imen .
Once comple ed he session, you will ecei e 5 e o
pa icipa ing, along wi h you ea nings co esponding
o he ounds, once con e ed in o eu os. Fo
con enience, he o al ea nings a e ounded up o he
nea es 50 cen s.
You will access he expe imen s a e eading hese
ins uc ions. When all pa icipan s ha e accessed, he
ounds will begin.
You a e going o pa icipa e in 4 expe imen s. Each
expe imen consis s o 15 ounds. Be o e s a ing each
expe imen , all he playe s, you included, will be
andomly loca ed in he nodes o he ne wo k shown
below.
3.2 de eloping 35
You posi ion in he ne wo k will be deno ed wi h he
le e ‘M’ ( o me). In he same way, wo di e en
nodes will be chosen as Sou ce (S) and Des ina ion
(D) espec i ely. Thei posi ion in he ne wo k will
be deno ed wi h he le e s ‘S’ and ‘D’. All he
playe s will emain in he same posi ion du ing each
expe imen o 15 ounds. In he same way, he sou ce
and des ina ion will emain in he same posi ion
h oughou each expe imen o 15 ounds. The playe s
will play he ole o in e media ies. A good mus be
anspo ed om S o Dgene a ing a bene i o 100
okens o all playe s in ol ed (S,D, and all nodes
in he pa h be ween hem). In e media ies ( ha is, he
playe s) simul aneously ha e o pos he ac ion o
hese 100 okens hey would like o cha ge i selec ed,
which mus be be ween 0 and 100 okens. You will ha e
60 seconds o pos you p ice. I you do no pos a
p ice, he compu e will decide o you: please do no
un ou you ime and make you own decision.
This is he sc een you will see in he i s ound
( his sc eensho is only an example):
Round 1 o se ies 1
The sum o p ices along any gi en pa h be ween Sand
Dde e mine a o al cos . Once all he in e media ies
ha e pos ed a p ice, he cheapes pa h (wi h lowes
o al cos ) om S o Dwill be selec ed. I he o al
cos o he cos cheapes pa h is less han o equal
o 100 okens, he good will be aken om S o D.
O he wise, ha is, i all he pa hs om S o Dcos
mo e han 100 okens, he e will be no deal and no
alue will be gene a ed. Ties a e b oken andomly, ha
is, i he e a e mo e han one cheapes pa h, one o
hem will be selec ed a andom.
36 pe o ming expe imen s
You payo in his ound will be:
a) I you a e loca ed on he selec ed cheapes pa h,
you will ecei e you p ice as payo . b) O he wise,
ha is, i you a e no on he selec ed pa h, you
will no ecei e any payo in ha ound. S and D
will ecei e, equally dis ibu ed, he es o he 100
okens.
F om he second ound on, you will be in o med abou
whe he he e was a deal in he p e ious ound, and
i so wha was he selec ed cheapes pa h, and he
cos s o his pa h. You will also be in o med abou
he cheapes pa h h ough you node ega dless o
whe he his was he selec ed cheapes pa h. The
selec ed pa h will be highligh ed by a dashed ed
line, while he cheapes pa h h ough you node will
be highligh ed by a blue solid line. No e ha he
cheapes pa h h ough you node may con ain loops,
i.e., i may pass mo e han one ime h ough some
nodes. Wi h his in o ma ion on he sc een, you mus
se a p ice o he cu en ound. A he end o each
expe imen , he posi ions o all playe s, he sou ce,
and he des ina ion will be andomly eassigned, and
a new expe imen o 15 ounds will begin.
This is he sc een you will see in he subsequen
ounds ( his sc eensho is only an example):
Round 4 o se ies 1
Please, click he below NEXT bu on o s a :
[NEXT]

3.3 es ing & ixing 37
3.3 es ing & ixing
“All code is guil y,
un il p o en
innocen .”
Anonymous au ho
When a i s e sion o he expe imen al so wa e is eady, i has o
be es ed se e al imes o inding possible p og amming e o s o
misspelled ex . Tes ing can gene a e new ideas o he ecogni ion
o new demands, which will be inse ed in o a new e sion. This
loop epea s un il so wa e is ecognized o be ok. Hope ully, he inal
e sion will be bug- ee.
3.4 unning
Las ly, a ba ch o expe imen s will be planned and pa icipan s will
be ec ui ed o he sessions. Ideally, a pilo is ini ially p og ammed
wi h a small subse o pa icipan s o e i y i some change in he
expe imen al se up would be needed o bene icial o he expe imen .
In ou wo k, mos o he imes, we ec ui ed pa icipan s h ough he
olun ee pool o he IBSEN p ojec (h p://www.ibsen.eu), which,
a he ime o w i ing, con ains 28234 egis e ed pa icipan s. Pa ici-
pan s ha e o sign an in o med consen o pa icipa e, besides hei
anonymi y is always p ese ed in he expe imen . Mo eo e , he call
o pa icipan s will occu only a e i has been checked and app o ed
by a esea ch e hics commi ee, ensu ing he p ocedu e is pe o med
ollowing he ele an guidelines and egula ions.
Fu he mo e, mone a y incen i es a e used o mo i a e pa icipan s,
and hey a e di ec ly ied o hei pe o mance in he game. Gi en
ha we a e no able o obse e hei o he in insic p e e ences, i is
easonable, ce e is pa ibus, o assume hey p e e a la ge payo o e
a smalle one. This p ocedu e ollows he me hodology o paying
pa icipan s om expe imen al economics, which is a a iance wi h
some o he ields, such as expe imen al psychology
7
. This p ac ical
de ail will none heless cons ain he numbe o pa icipan s, as an
expe imen al budge is limi ed. Usually, paymen pe subjec is cal-
cula ed such ha he a e age payo is a ound he coun y a e age
hou ly wage. Acco dingly, a he end o he expe imen pa icipan s
will be paid in cash in he case o a lab expe imen , while in online
expe imen s paymen is o en done by using an ex e nal se ice such
as PayPal8.
In a lab expe imen , people can en ol h ough open calls in he
IBSEN ec ui men pla o m, and hey a e ins uc ed o a end a a
scheduled ime and place. As some people migh no be able o a end,
pa icipan s a e usually o e ec ui ed. Un o una ely, depending on
he expe imen al se up, ex a pa icipan s migh no be able o play, in
his case, hey will be paid he game expec ed payo and be o e ed
apologies. I is no a pe ec solu ion, bu s ill be e han no pe o m-
7See [30, Chap e 11] o an o e iew and discussion in his subjec .
8h ps://www.paypal.com/
38 pe o ming expe imen s
ing he session. Pa icipan s a e o en paid acco ding o a show-up
ee (a ixed amoun gua an eeing ha hey ecei e a leas some hing)
plus some quan i y in he unc ion o hei ea nings in he game.
Expe imen s can also be pe o med online, wi h each pa icipan
accessing he pla o m emo ely. This app oach educes con ollabili y
o he expe imen bu allows a highe lexibili y in he numbe o
pa icipan s. As pa icipan s’ e o s a e educed ( hey can play om
hei homes o jus some minu es), he paymen can ollow a lo e y,
such ha only some ac ion o he playe s will be paid some subs an-
i e amoun . Hence, by his app oach, he e is i ually no limi a ion
in he maximum numbe o pa icipan s. None heless, pa icipan s
p obably do no ha e he same incen i es as when paid di ec ly by
hei ea nings in he game. Thus, o mo i a e hem, he lo e y selec s
winne s in p opo ion o hei pe o mance in he expe imen . The
main issue wi h online expe imen s is ha , un o una ely, i is no
i ial o synch onize play among pa icipan s, which makes epea ed
games ha d o be pe o med, al hough some solu ions a e possible
[133].
When all he expe imen al sessions ha e been pe o med, backup
copies o he expe imen al da a a e made. The nex s eps a e p ep o-
cessing and analysing he da a, which will gene a e esul s such as
he ones p esen ed in he ollowing chap e s.
Pa II
EXPERIMENTS AND THEORETICAL MODELS
4.1 a common pool o dynamic esou ces 47
o he no- eco e y h eshold. None heless, he o es ’s s a e could be
moni o ed a all imes ia a de ailed in e ace (Fig. 4.2). Pa icipan s
could also compa e hei own pe o mance in e ms o e o , yield,
and p o i wi h o he s. Using his se up, we pe o med expe imen al
sessions in wo pool o pa icipan s: i) 96 unde g adua e s uden s
in Xi’an, China; ii) 90 indi iduals om he gene al popula ion in
Za agoza, Spain. Pa icipan s we e ins uc ed ha hey would ecei e
a mone a y payo ied o hei end p o i in he game. The esul ing
payo s amoun ed o an a e age o
U
62.6in China and
e
15.1in Spain,
u he de ails a e shown in a.
Figu e 4.2:Sc eensho o he gameplay page
. We di ided he gameplay
page in o h ee dis inc pa s: esou ce s a e,pe o mance e iew,
and decision making. The esou ce s a e pa consis ed o a game-
like isualiza ion o he i ual o es plus a s a us ( esp., p og ess)
ba showing he numbe ( esp., ac ion) o emaining ees. The
pe o mance e iew pa ocused on e o , ha es , and p o i
ba cha s wi h a ho e e ec such ha mo ing he cu so o e
any o he ba s igge ed a ool ip displaying he co esponding
nume ical alue. Las ly, he decision-making pa comp ised a
simple inpu o m asking o he desi ed e o and a message
box ha au oma ically con e ed e o in o he ha es ing cos .
Final decisions had o be con i med by clicking he Nex bu on.
Fo he ac ual sessions o he expe imen , we used Chinese o
Spanish ansla ions.

48 collec i e ac ion p oblems
4.1.3Resul s
We used he MSY alue as na u al pe o mance classi ie o 16 Chi-
nese and 15 Spanish playe g oups. Namely, we de ined he op imal
exploi a ion as any numbe o ees le o cu ing a e 50 ounds
ha was wi hin
±
10% o he MSY numbe (136–166 ees). Only one
g oup om each o he coun ies was able o op imally exploi he
esou ce. None o he g oups unde exploi ed he esou ce by ending
he expe imen abo e he op imal ange, whe eas a o al o 14 Spanish
and 15 Chinese g oups o e exploi ed he esou ce by ending below
his ange. The i ual o es ’s ime e olu ion sugges s ha he o me
g oups pe o med much wo se (Fig. 4.3A). Se en g oups om Spain
d o e he numbe o ees in he o es below he no- eco e y h esh-
old (
=
100 ees), whe eas only one g oup om China did he same,
and i did so only in he las ound o he game.
Ne e heless, a ime-se ies eg ession analysis e eals ha mul iple
Chinese g oups kep deple ing he esou ce, and gi en mo e ime,
would ha e likely c ossed he no- eco e y h eshold oo (Fig. 4.3B).
Deno ing wi h
R
he i ual o es ’s s a e a ime s ep
, whe e
0=
20 ≤ ≤50
, we i ed he ollowing model o he ime-se ies da a
pe aining o he g oups who o e exploi ed, bu did no deple e he
esou ce.
R =c0+c1( − 0)+(1+c2)R −1+c3(R −1−R −2)(4.5)
Pa ame e s
c0
,
c1
, and
c3
co espond o he cons an , he end, and
he au o- eg essi e e m, espec i ely. Pa ame e
c2
e lec s ime se ies
s a iona i y. The esul s o he Sus ained g oups a e shown in Table 4.1.
Six addi ional Chinese g oups, , bu none o he Spanish g oups, kep
deple ing he esou ce (
c1<0
) un il he end o he expe imen . Gi en
mo e ime, hese g oups would ha e likely c ossed he no- eco e y
h eshold.
A o al o se en g oups on each side sus ained he o e exploi ed e-
sou ce, i.e., hei exe ed e o was sus ainable, bu hey kep ea ning
subop imal p o i s (Fig. 4.3C). In e es ingly, none o he g oups man-
aged o ully e e se he decline and inish wi h a eco e ing esou ce
(
c1>0
). A conclusion is ha he ou come in bo h coun ies, especially
when conside ing oge he he g oups who kep deple ing o al eady
deple ed he esou ce ( ed ec angle in Fig. 4.3C), was ema kably
simila and a he dismal.
4.1.3.1Beha iou al Model
To unde s and how pa icipan s we e beha ing in he expe imen , we
cons uc ed a s a is ical eg ession model o pa icipan s beha iou .
The model’s dependen (i.e., esponse) a iable was e o , which
4.1 a common pool o dynamic esou ces 49
0
100
200
300
400
Round
Resou ce
Op imal O e exploi ing Deple ed
China
100
125
150
175
200
Round
Resou ce
20
A
Spain
Spain
China
30 40 50 20 30 40 50
Unde exploi ed
Op imal
O e exploi ed
Reco e ing
Sus ained
Deple ing
Deple ed
China Spain
20 30 40 50
10020 30 40 50
100
Deple ing Sus ained
B
C
Figu e 4.3:O e exploi a ion is a end. A,
Ou o 16 Chinese and 15 Span-
ish g oups who exploi ed he common-pool esou ce, only one
g oup om each coun y was able o keep he esou ce a an
op imum. We de ined he op imum as
±
10% om he numbe o
ees maximizing he sus ainable yield (
≈
151 ees). Wo yingly,
all o he g oups o e used he esou ce, and wha is mo e, one Chi-
nese and se en Spanish g oups deple ed i below he no- eco e y
h eshold (
=
100 ees).
B,
Chinese g oups seemingly do be e
han hei Spanish coun e pa s, bu is his uly so? To examine
he likely a e o o e exploi ed, bu non-deple ed i ual o es s
beyond ound 50, we es ed whe he a e a ansi o y pe iod o
abou 20 ounds he numbe o ees was eco e ing, sus ained,
o deple ing (Table 4.1). We ound ha six Chinese g oups kep
deple ing he esou ce un il he e y end, while se en g oups
om each coun y sus ained a ela i ely cons an numbe o ees.
No g oups om ei he coun y managed o o e u n he nega i e
end and allow he esou ce o eco e .
C,
No ably, none o he
g oups om he wo coun ies unde exploi ed he esou ce, while
a o al o se en g oups om each coun y deple ed o would ha e
likely ended up deple ing he esou ce ( ed ec angle).
we ied o explain using ollowing independen (i.e., explana o y)
a iables:
•The i ual o es ’s s a e
: we expec ed pa icipan s o exhibi
di e en beha iou s when he esou ce is abundan as opposed
o when he esou ce is deple ed.
50 collec i e ac ion p oblems
•Lagged own e o s
: included o accoun o po en ial au oco e-
la ions in he play o indi idual pa icipan s; posi i e au oco e-
la ions, in pa icula , would be an indica ion o decision-making
“ine ia” whe eby high ( esp., low) pas e o s inc ease he likeli-
hood o high ( esp., low) p esen e o .
•Lagged a e age e o s o o he s
: included o accoun o po-
en ial c oss-co ela ions as a e lec ion o mu ual in luences
be ween pa icipan s.
Model pa ame e s, i.e., eg ession coe icien s, accompanying hese
h ee ypes o explana o y a iables we e kep cons an among pa ici-
pan s om a gi en coun y, hus cha ac e izing a collec i e beha iou al
ocus. Indi idual di e ences en e ed he model by allowing cons an
e ms and esidual a iances o be pa icipan -speci ic ia ixed e -
ec s, and ia pa icipan -speci ic esidual a iances, espec i ely. We
in e p e ed he o me as indi idualis ic p opensi ies o exe e o
i espec i e o he s a e o he explana o y a iables. Acco dingly, play-
e s wi h la ge ixed e ec s we e mo e likely o cu ees e en i he
numbe o ees le o logging was small, o e en i o he playe s
e ained om logging. Residual a iances, by con as , quan i ied
indi idualis ic p opensi ies o andomly a y e o . We in oduced
pa icipan -speci ic esidual a iances because we expec ed ha hu-
man pa icipan s would exhibi a wide spec um o beha iou s. Wi h
hese ideas in mind, a gene al model o mula ion was
Ti( )=βRR( )+
S1
∑
s=1
β−s
TTi( −s)+
+
S2
∑
s=1
β−s
hTihT( −s)i+βi+ei( ),
(4.6)
whe e dependen a iable Ti( )co esponds o he i h playe ’s e o
in ound
. Among he h ee ypes o explana o y a iables,
R( )
is
he i ual o es ’s s a e in ound
,
Ti( −s)
is he
i
h playe ’s lagged
e o
s
ounds p io o
, and
hT( −s)i
is he lagged a e age e o
o o he s, also
s
ounds p io o
. The numbe s o lagged e ms in
he model,
S1
and
S2
, we e unknown p io o pa ame e es ima ion.
Quan i y
βi
is he model’s cons an e m, i.e., a ixed e ec speci ic
o he
i
h playe . Finally,
ei( )
a e he model’s no mally dis ibu ed
esiduals wi h ze o mean and esidual a iance
σ2
i
, again speci ic o
he
i
h playe . Assuming he no mal dis ibu ion he e implied a lack
o au oco ela i e s uc u e in esiduals. This was easonable gi en
ha he lagged own e o s in Eq. (4.6) should accoun o po en ial
au oco ela ions in playe decisions.
The model is able o explain he pos ed e o s. Fig. 4.4shows
ha p edic ions i obse a ions well as i is seen in obse a ion- s-
p edic ion sca e plo s: poin s ga he a ound he “diagonal”, i.e., he
4.1 a common pool o dynamic esou ces 51
-2 -1 0 1 2
-2
-1
0
1
2
S anda dised obse a ions
P edic ions
-2 -1 0 1
-2
-1
0
1
P edic ions
A B
China Spain
S anda dised obse a ions
Figu e 4.4:Beha iou al eg ession pe o mance.
Obse a ion- s-p edic ion
sca e plo s and he accompanying s a is ics in ui i ely display
and quan i y he pe o mance o s a is ical eg ession models.
In such plo s, he sca e ed poin s should g oup a ound he “di-
agonal”, meaning ha he line i ed o hese poin s should be
s a is ically indis inguishable om he line wi h in e cep
0
and
slope
1
.
A,
Fo he Chinese da a, he in e cep is indeed indis-
inguishable om 0(es ima e -0.0018;95% CI
[−0.0221,0.0186]
),
bu he slope is sligh ly lowe han 1(es ima e 0.9544;95% CI
[0.9279,0.9809]
), hus sugges ing ha he model somewha o e -
p edic s ( esp., unde p edic s) low ( esp., high) e o s. The coe -
icien s o de e mina ion is
R2=0.592
.
B,
Fo he Spanish da a,
hese mino pe o mance issues disappea because no only he
in e cep is indis inguishable om 0(es ima e -0.0006;95% CI
[−0.0193,0.0180]
), bu also he slope is indis inguishable om 1
(es ima e 0.9888;95% CI
[0.9659,1.0116]
). The coe icien s o de-
e mina ion is
R2=0.689
. Due o a la ge numbe o da a poin s
(
>
4000 pe plo ), we g ouped hem in o bins as e enly as possible,
and hen displayed he medians (ci cles), he in e qua ile anges
(boxes), he limi s ha would encompass 99.3% o no mally dis-
ibu ed da a (whiske s), and “ou lie s” (indi idual poin s).
line wi h in e cep 0and slope 1. The coe icien s o de e mina ion
u he indica e ha he model accoun s o nea ly 60% ( esp., 70%) o
he o al a iance in he Chinese ( esp., Spanish) da a.
The beha iou al eg ession model o e s plausible explana ions on
why ou comes in China and Spain we e simila ly dismal. We ound
among he Spanish pa icipan s ha , while he i ual o es ’s s a e
and he a e age e o o o he s in o m decisions on he cu en e o ,
a key de e minan in his con ex is one’s own lagged e o s (Fig. 4.5A).
We hus wi nessed a o m o decision-making “ine ia” by which pas
choices hea ily weigh on he p esen choice. The e ec is signi ican
up o i e lags in he pas . In e es ingly, he Chinese pa icipan s
exhibi quali a i ely he same beha iou al pa e ns; again he o es ’s
s a e and he a e age e o o o he s in o m decisions, bu hese a e
much less in luen ial han one’s own lagged e o s (Fig. 4.5B). E en
quan i a i ely he esul s a e ema kably simila because only he e ec
52 collec i e ac ion p oblems
0.0
0.1
0.2
0.3
0.4
0.5
Pa ame e alues
Spain
-1 -2 -3 -4 -5 -1
RTTTTT⟨T⟩
-0.2
-0.1
0.0
Adjus men s
China
A
B
βββββββ
Δ Δ Δ Δ Δ Δ Δ
-1 -2 -3 -4 -5 -1
RTTTTT
βββββββ
⟨T⟩
Figu e 4.5:Beha iou al pa e ns behind he demise o he commons a e
obus ac oss na ions. A, Es ima ed pa ame e alues show ha
while he i ual o es ’s s a e (pa ame e
βR
) and he e o o
o he s (pa ame e
β−1
hTi
) in o m pa icipan decisions, he Spanish
pa icipan s exhibi a o m o decision-making “ine ia” by which
he cu en e o s ongly e lec s p e ious own e o s (pa am-
e e s
β−1
T
o
β−5
T
). The e ec is signi ican up o i e lags in he
pas . He e, shown a e he pa ame e es ima es (poin s) and he
co esponding 95% con idence in e als (e o ba s).
B,
Adjus -
men s o he Spanish pa ame e alues o i he da a om China
indica e ha he Chinese pa icipan s exhibi he same decision-
making “ine ia” as hei coun e pa s in Spain. The e ec is only
sligh ly weake a lag 2(pa ame e
∆β−2
T
), bu o he wise s a is i-
cally indis inguishable be ween he wo coun ies. The e o o
o he s also has a s a is ically indis inguishable e ec . The only
quali a i e di e ence is e lec ed in he
∆βR
pa ame e , e ealing
ha he Chinese ( esp., Spanish) pa icipan s exe mo e e o
when he esou ce is sca ce ( esp., abundan ). This is consis en
wi h a gen le ( esp., s eepe ) ini ial decline o he esou ce in
China ( esp., Spain). The nega i e ela ionship be ween esou ce
abundance and e o in China backs up ou conclusion om he
ime-se ies analysis (Table 4.1) ha six addi ional Chinese g oups
would ha e e en ually deple ed he esou ce.
o own e o a lag 2is sligh ly weake among he Chinese pa icipan s,
while he e ec a o he lags is s a is ically indis inguishable be ween
he wo coun ies (Fig. 4.5B). The same is ue o he a e age e o
o o he s. Based on hese esul s, one conclusion o ce i sel upon
us. Gi en ha a decen numbe o pa icipan s om as ly di e en
coun ies pe o med in a ema kably simila ashion, beha iou al
pa e ns behind he demise o he commons a e, i no uni e sal, hen
a leas obus o a my iad o con ounding ac o s.

4.1 a common pool o dynamic esou ces 53
The one subs an ial di e ence be ween he wo coun ies is ha
he i ual o es ’s s a e co ela es nega i ely wi h he e o o he
Chinese, bu posi i ely wi h he e o o he Spanish pa icipan s
(Fig. 4.5). The o me s a exploi ing he esou ce mo e cau iously, bu
hen compensa e o a s eady esou ce deg ada ion wi h mo e e o .
The la e , by con as , s a mo e agg essi ely, bu hen cu ail hei
zeal in esponse o a disappea ing esou ce. The desc ibed di e ence
be ween he wo coun ies helps o explain he as e esou ce deple-
ion in Spain han in China (Fig. 4.3), and is ully consis en wi h he
clus e ing esul s (Fig. 4.7). Analysing he pa icipan -speci ic model
e ms u he complemen s his explana ion (Appendix Sec ion a.1.1).
Me iculous eg ession diagnos ics show ha we a oided he common
pi alls o his ype o analysis, and hus ha he model’s esul s a e
c edible (Appendix Sec ion a.1.2).
4.1.3.2Clus e ing
To gain a deepe insigh abou he di e ences among pa icipan s
om bo h coun ies, we eso ed o he
k
-means clus e ing algo i hm.
We used ou quan i a i e cha ac e is ics as a basis o clus e ing wi h
he idea ha hese cha ac e is ics would e lec beha iou s exhibi ed
in each o he wo hal es o he game expe imen . They a e cumula i e
e o s and o al p o i s om bo h he i s and he second hal o
he game aken sepa a ely. We su mised ha beha iou al changes
be ween he wo game hal es would be o pa icula in e es gi en
ha he esou ce s a e de e io a es as ime passes, causing p o i s o
decline as well.
In such an analysis, he op imal numbe o clus e s in o which
he da ase should be pa i ioned is no a p io i known. As many
as 11 di e en op imali y measu es o add essing his p oblem a e
commonly ound in li e a u e [170]. Among hese, we selec ed he sil-
houe e me hod o i s concep ual cla i y [171]. The silhoue e me hod
con as s clus e cohesion (i.e., how simila da a poin s a e o hei e-
spec i e clus e s) o clus e sepa a ion (i.e., how dissimila da a poin s
a e o o he clus e s). The la ge he a e age silhoue e alue o he
da ase depending on he numbe o clus e s, he be e is he gi en
pa i ioning in o clus e s. Using he silhoue e me hod on Chinese and
Spanish da a sepa a ely, we i s ound ha he Chinese pa icipan s
a e bes pa i ioned in o h ee clus e s (Fig. 4.6A). The Spanish case
is somewha ambiguous because pa i ioning in o wo clus e s yields
only a ma ginally la ge a e age silhoue e alue han pa i ioning
in o ou clus e s (Fig. 4.6B). A close inspec ion o bo h op ions e-
eals ha he esul s a e mo e in o ma i e in he con ex o ou game
expe imen when he Spanish pa icipan s a e pa i ioned in o ou
clus e s.
The Chinese pa icipan s exhibi h ee p ominen beha iou s b oadly
desc ibable as agg essi e, mode a e, and imid (Fig. 4.7A). E o and
54 collec i e ac ion p oblems
B
Op imum Local maximum
0.4
Op imum
A g. silhoue e wid h
0.3
0.2
0.1
0.0
0.4
0.3
0.2
0.1
0.0
1
Numbe o clus e s
2 3 4 5 6 7 8 9 10
Numbe o clus e s
1 2 3 4 5 6 7 8 9 10
A
China Spain
Figu e 4.6:De e mining he op imal numbe o clus e s wi h he a e age
silhoue e wid h.
The silhoue e alue is a measu e o how well
a da a poin i s o i s own clus e as opposed o o he clus e s
(cohesion s. sepa a ion), anging om -1 o a poo i o 1 o
a good i . A e aging silhoue e alues o e an en i e da ase
p oduces an agg ega e measu e, called he a e age silhoue e
wid h, o how well he da a ha e been clus e ed. This measu e is a
unc ion o he numbe o clus e s. The bes clus e ing is achie ed
wi h he numbe o clus e s o which he a e age silhoue e
wid h is maximal.
A,
Fo he Chinese da a, he op imal numbe
o clus e s is h ee.
B,
Fo he Spanish da a, pa i ioning in o wo
o ou clus e s yields nea ly an equal a e age silhoue e wid h.
We op ed o he la e numbe because ou clus e s p o ed o
be e y in o ma i e in he con ex o ou game expe imen .
p o i g adually dec ease om agg essi e o mode a e o imid playe s.
Rema kably, pe o ming independen clus e ing on he Spanish da a
e eals conside ably simila beha iou s pa e ns, wi h he addi ion
o a ou h one, dubbed lipping (Fig. 4.7A). This las beha iou is
agg essi e o mode a e in he i s hal o he game, bu u ns imid
in he second hal . We u he mo e ound ha agg essi e and imid
beha iou s a e almos equally abundan in bo h coun ies, encompass-
ing
≈
25% and
≈
10% o playe s, espec i ely (Fig. 4.7A). The Chinese
case is enough o demons a e ha wi h such a dis ibu ion o playe s
o e exploi a ion is he mos likely ou come. Adding he a he agg es-
si e i s -hal beha iou o lipping playe s o his only con ibu es
o he as e esou ce decline in Spain han in China, hus helping
o explain why mul iple Spanish g oups managed o e en c oss he
no- eco e y h eshold.
P ominen playe beha iou s show wha sepa a es op imal ha es -
ing om sus ained o e exploi a ion om esou ce deple ion. G oups
who ha es op imally ha e almos he same composi ion in bo h
coun ies (Fig. 4.7B), cha ac e ized by a ela i e sca ci y o agg essi e
(
≈
17%) and a disp opo ional abundance o imid (
≈
33%) playe s.
G oups esponsible o sus ained o e exploi a ion also ha e almos he
same composi ion in bo h coun ies (Fig. 4.7B), only he e agg essi e
playe s a e abundan (
≈
30%) and imid playe s a e sca ce (
≈
7%). The
Chinese g oup who deple ed he esou ce has he highes p opo ion
o agg essi e playe s (
≈
33%) and no imid ones wha soe e (Fig. 4.7B),
while he co esponding Spanish g oups ha e only a ew s ay imid
playe s (
≈
2.5%). The la e g oups also ha bou almos all lipping
4.1 a common pool o dynamic esou ces 55
0.6
1.2
1.8
Cumula i e
China
Spain
A
G
G
R
E
S
S
I
V
E
M
O
D
E
R
A
T
E
T
I
M
I
D
F
L
I
P
P
I
N
G
E1
A
M
T
F
gg essi e
ode a e
imid
lipping
A
Effo (1 hal )
s
Effo (2 hal )
nd
P ofi (1 hal )
s
P ofi (2 hal )
nd
E2
P1
P2
E1
P1
E2P2
E1
P1
E2P2
E1
P1
E2P2
E1
P1
E2P2
E1
P1
E2P2
E1
P1
E2P2
E1
P1
E2P2
China
Spain
F ac ion
0.00
0.25
0.50
0.75
1.00
Op imal
Sus ained
0.00
0.25
0.50
0.75
1.00
Deple ed
Spain
0.00
0.25
0.50
0.75
1.00
Op imal
Sus ained
Deple ed
Deple ing
China
B
Figu e 4.7:In e play o p ominen beha iou s explains o e exploi a ion.
A,
Running a clus e ing algo i hm on da a om China and Spain
sepa a ely, we iden i ied h ee ( esp., ou ) dis inc p ominen
beha io s among he Chinese ( esp., Spanish) pa icipan s. Apa
om he beha io unique o Spain, he h ee emaining beha io s
a e nea ly iden ical i espec i e o he coun y. In e ms o e o ,
hese can be desc ibed as agg essi e, mode a e, and imid. Wi h
he scale se ela i e o he MSY e o and he co esponding
p o i , we see ha agg essi e playe s exceed he MSY e o by
o e 80%, ea ning la ge p o i s in he i s hal o he game. Mod-
e a es s ay close o he MSY e o , none heless exceeding i by
abou 20%. Timid playe s s a cau iously a 60% o he MSY
e o and, unlike agg essi e o mode a e playe s, educe e o in
esponse o esou ce de e io a ion. The ou h Spanish beha io
lips om an agg essi e ini ial s ance o a imid subsequen one,
ea ning almos no p o i la e in he game.
B,
O e all abundance
o agg essi e and imid playe s is ema kably simila ac oss coun-
ies (le panel), as is he abundance o hese playe s in g oups
ha played op imally and g oups ha sus ained he esou ce in
an o e exploi ed s a e (middle and igh panels). Op imal play
clea ly equi es a much mo e a o able agg essi e- o- imid a io
han is p esen in he o e all abundance, hus explaining o e -
exploi a ion. The lipping beha io is nea ly exclusi e o g oups
ha deple ed he esou ce in Spain, indica ing ha many playe s
become esponsi e o he esou ce s a e only when i is oo la e.
playe s (
≈
45%), who ac a he agg essi ely in he i s hal o he
game and con ibu e o esou ce decline alongside agg essi e playe s
56 collec i e ac ion p oblems
(
≈
21%). The ou iden i ied p ominen beha iou s hus go a long
way in explaining he sub le di e ences in he i ual o es ’s ime
e olu ion be ween China and Spain, as well as he o e all bias owa ds
o e exploi a ion. Pa icula ly in iguing is a numbe o ema kable
simila i ies be ween he wo coun ies hin ing a he exis ence o obus
beha iou al pa e ns behind he demise o he commons.
4.1.4Discussion
Ha ing asked pa icipan s om China and Spain o exploi a i ual
o es while acing he same epis emic and socio-economic obs acles as
eal-wo ld ope a o s, we ound ha seemingly di e en ou comes a e,
in ac , ema kably simila and bode ill o he a e o common-pool e-
sou ces. An explo a o y da a analysis in he o m o clus e ing e eals
ha he esul s a e la gely a ibu able o h ee beha io al ypes (also
called pheno ypes in he li e a u e), dubbed agg essi e, mode a e, and
imid. Al hough he na u e o he game in ou expe imen is di e en
om hose in p e ious expe imen s ha epo beha io al pheno ypes
[172–174], we see clea pa allels be ween agg essi e, mode a e, and
imid playe s he ein and de ec o s, coope a o s, and supe coope a o s
in Re . [174], espec i ely. The consis ency o p e iously iden i ied
beha io al pheno ypes [173,174] u he sugges s ha he ypes we
ound a e also a consis en ea u e o human beha io a he han a
peculia i y o he speci ic expe imen al se up. In ac , ha ing wo ked
wi h wo geo-socially dis an popula ions, and in a no el and ela i ely
complex con ex , ou esul s go a long way in o i ying he conclu-
sions o he ci ed s udies ha human beha io s in social dilemmas a e
di isible in o a small numbe o s able pheno ypes.
A p e ious s udy [175] using a simila se up, albei wi h explici e-
sou ce “dynamics” such ha e e y 10 s anding ees yielded one new
ee pe ound, epo ed he ou come o he game expe imen com-
pa ed o o he si ua ions. He e, by con as , we implemen ed a mo e
ealis ic dynamic—whose quali a i e cha ac e is ics, bu no quan i a-
i e de ails, a e known by he pa icipan s—and iden i ied collec i e
beha io al mechanisms ha unde pin decisions on exploi a ion, hus
poin ing o one main culp i o simila ly dismal ou comes in bo h
coun ies. Ins ead o p io i izing he esou ce s a e when deciding he
cu en e o , pa icipan s ope a e unde decision-making “ine ia”
by which hey a e much mo e conce ned wi h hei own pas e o s.
A su p ising aspec he e is ha his mechanism ma e ializes in wo
popula ions no only sepa a ed geog aphically, bu also in luenced by
a my iad o con ounding ac o s such as age, educa ion, and cul u e.
The Chinese pa icipan s sha ed compa a i ely young age, exposu e
o highe educa ion, and upb inging in he mids o a quin essen ial
Eas Asian cul u al he i age. The Spanish pa icipan s mi o ed he
gene al popula ion in e ms o age and educa ional backg ound, while
4.2 a ge s and biases:a collec i e- isk social dilemma be ween wo coun ies 63
Dependen a iable:
Playe Con ibu ion
Spanish 0.036 (0.030)
In o med −0.081∗∗ (0.033)
LT 0.010 (0.021)
Round −0.009∗∗∗ (0.003)
In o med x Spanish 0.081∗(0.043)
LT x Spanish −0.053∗∗ (0.027)
Cons an 0.558∗∗∗ (0.027)
Obse a ions 1,920
R20.018
Adjus ed R20.015
F S a is ic 35.875∗∗∗
No e: ∗p<0.1;∗∗p<0.05;∗∗∗p<0.01
Table 4.3:Homogeneous sessions eg ession
. Es ima es om a andom e -
ec s model o he Homogenous sessions’ pa icipan s. Robus
s anda d e o s a e clus e ed a he indi idual le el.
˜
Ci =β0+β1In o medi+β2Spanishi+
β3In o medi∗Spanishi+
β4LT40 +β5LT40 ∗Spanishi+
β6Round +
αi+ei
(4.8)
In his case,
˜
Ci
co esponds o he no malized con ibu ion and
LT40
is a dummy a iable con olling o he a ge o he pa icipan ’s
g oup (
LT =20
is he e e ence g oup) – i.e, i equals o 1in he
LT40
ea men and 0 o he wise.
The esul s o he eg ession o he Homogeneous and He e o-
geneous sessions a e shown in Tables 4.3and 4.4, espec i ely. The
decay in con ibu ions wi h ime is common o bo h session ypes,
as gene ally i is obse ed in epea ed Public Goods Games [46,48].
In he homogeneous sessions, Chinese pa icipan s con ibu ed less
when in o ma ion o Spania d’s na ionali y was disclosed (-0.08 in
con ibu ions pe ound). In e es ingly, his e ec is no obse ed o
Spanish pa icipan s (0=0.08-0.08), and al hough hei con ibu ions
a e smalle when hei g oup had a local a ge , hey we e s ill a ound

64 collec i e ac ion p oblems
Dependen a iable:
No malized Playe Con ibu ion
Spanish 0.102 (0.150)
In o med 0.021 (0.072)
(LT =40)−0.162∗∗∗ (0.035)
Round −0.035∗∗∗ (0.008)
In o med x Spanish −0.084 (0.136)
(LT =40)x Spanish −0.152∗(0.084)
Cons an 1.314∗∗∗ (0.083)
Obse a ions 1,920
R20.056
Adjus ed R20.053
F S a is ic 112.892∗∗∗
No e: ∗p<0.1;∗∗p<0.05;∗∗∗p<0.01
Table 4.4:He e ogeneous sessions eg ession
. Es ima es om andom-
e ec s eg ession o he He e ogeneous sessions’ pa icipan s.
Robus s anda d e o s a e clus e ed a he indi idual le el.
4.2 a ge s and biases:a collec i e- isk social dilemma be ween wo coun ies 65
One Ta ge
Two Ta ge s
Unin o med
In o med
0.00 0.25 0.50 0.75 1.00 0.00 0.25 0.50 0.75 1.00
0.0
2.5
5.0
7.5
10.0
0.0
2.5
5.0
7.5
10.0
Mean Con ibu ion by Pa icipan
China Spain
Figu e 4.9:Dis ibu ions o playe s’ a e age con ibu ion in he Homoge-
neous sessions.
His og am o playe s’ mean con ibu ions ac-
co ding o he in o ma ion p o ided and ea men in he Ho-
mogeneous sessions. The p esence o pa icipan s wi h a e ages
smalle han he ai esul s in a educ ion o he g oup’s a e age
con ibu ion.
he ai (0.51=0.56-0.05). These e ec s a e ela i ely small bu hey
migh be enough o lead g oups o collapse, as hei baseline con i-
bu ions a e only sligh ly o e he ai (0.56). Impo an ly, he e ec o
in o ma ion migh be enough o g oups in he In o med ea men
o be close o he agedy o he commons. This is e idenced by
compa ing he o al con ibu ions in each condi ion, which indica es
ha hey we e smalle when pa icipan s we e in o med (one-sided
unequal a iances - es :
9.1 =−2.3, P=0.023
), hough wi h modes
s a is ical powe . Likewise, compa ing he means o he wo coun ies
g oups when playing oge he sugges ha Chinese g oups’ o al con-
ibu ions we e signi ican ly smalle han om Spanish (one-sided
unequal a iances pai ed - es :
7=2.5, P=0.04
). These di e ences
a e due o some pa icipan s ha ing pal y mean con ibu ions in he
In o med sessions, as shown by Fig. 4.9. Wi hou in o ma ion, mos
pa icipan s will likely con ibu e he ai ; wi h in o ma ion, howe e ,
some o hem will ee ide.
This pa e n sugges s ha Chinese pa icipan s migh be less willing
o con ibu e when hey know hey a e playing ‘agains ’ Spanish pa -
icipan s. This hypo hesis, howe e , is unsuppo ed by he esul s o
he He e ogeneous sessions: hey indica e no di e ence be ween Span-
ish and Chinese pa icipan s wi h espec o he disclosed in o ma ion.
Na u ally, i shows ha he ela i e con ibu ions a e smalle when pa -
icipan s ha e la ge a ge s, a likely esul o ha ing a highe oll on
hei endowmen . In his case, he Spanish pa icipan s seem o ha e
66 collec i e ac ion p oblems
20
40
Unin o med
In o med
0.00 0.25 0.50 0.75 1.00 0.00 0.25 0.50 0.75 1.00
0.0
2.5
5.0
7.5
0.0
2.5
5.0
7.5
Mean Con ibu ion by Pa icipan
China Spain
Figu e 4.10:Dis ibu ions o playe s’ a e age con ibu ion in he He e o-
geneous sessions.
His og am o playe s’ mean con ibu ions
acco ding o he in o ma ion p o ided and he g oup a ge in
he He e ogeneous sessions. Le ( esp. igh ) panels co espond
o g oups wi h a a ge o 20 ( esp. 40).
con ibu ed less when hey we e obliged o make highe con ibu ions
han he o he g oup (-0.15), howe e , we a e no able o dis inguish
his om an expe imen al a e ac . In he He e ogeneous sessions,
Spanish pa icipan s always s a ed wi h a la ge a ge , which migh
ha e induced hem o con ibu e less, which is no he case o Chinese
pa icipan s. Thus, i emains an open ques ion whe he his e ec is
alid. None heless, i is ema kable ha playe s om bo h coun ies
complied adequa ely wi h he inequi y, e en i we conside he nega-
i e e ec on he Spanish pa icipan s’ con ibu ions (1=1.31-0.16-0.15).
Cu iously, p o iding in o ma ion seem o ha e clus e ed he con i-
bu ions a ound he a ge in he He e ogeneous sessions, as shown
by Fig. 4.10. When playe s did no know he o he g oup na ionali y,
hei a e age con ibu ions sp ead almos uni o mly o e he whole
possible ange, especially o Spania ds. Sugges ing ha unknowing
he o he coun y na ionali y migh in luence he appea ance o bo h
ee- iding and al uis ic beha iou .
4.2.2Discussion
The ou comes o Spanish and Chinese pa icipan s while playing
a collec i e- isk social dilemma does no seem o be in luenced by
whe he a ge s a e homogeneously o he e ogeneously dis ibu ed
among hem. Ou analysis indica es ha , in gene al, mos pa icipan s
will con ibu e a ound he ai , excep by some pa icipan s con ibu -
4.2 a ge s and biases:a collec i e- isk social dilemma be ween wo coun ies 67
ing less in he In o med sessions. This leads o a educ ion in he o al
con ibu ions o Chinese pa icipan s, aising he isk o hei g oups
no mee ing he a ge in he Homogeneous sessions. No ably, his
e ec is no obse ed in he He e ogeneous sessions, indica ing ha ,
al hough ou comes a e simila , pa icipan s migh eac o in o ma ion
di e en ly in bo h expe imen al se ups. In gene al, none heless, all
pa icipan s seem o con ibu e a ound o o e he ai , e en when
hey ha e he bu den o a la ge a ge . Spania ds’ con ibu ion is
smalle han he Chinese’s in his la e case – i.e.,
LT40
ea men in
he He e ogeneous sessions – bu no enough o nulli y his end.
Mo eo e , in ou se up g oups could also ha e a local h eshold,
implying ha pa icipan s a e conce ned wi h wo g oups, one wi h
12 pa icipan s and a subg oup wi h 6pa icipan s, which in u n
could inc ease he likelihood o eaching he a ge acco ding o some
hypo heses [187]. Ne e heless, we obse e jus a small e ec in he
o he di ec ion o he Spanish pa icipan s, i.e., hey con ibu e less
when a local a ge was in oduced in he second ea men o he
Homogeneous sessions. Seemingly, hus, con ibu ions can be smalle
when a local a ge is p esen . Howe e , u he eplica ions a e neces-
sa y o con i m whe he his esul is a ec ed by o de e ec s, as in
ou se up pa icipan s always played wi h a local a ge a e playing
he GT ea men . Ei he way, he Chinese pa icipan s a e no a ec ed
by he o de o local a ge in he Homogeneous sessions, con ibu ing
a ound he same in bo h ea men s.
I seems pa icipan s espond well o he a ge s imposed on hem,
e en when hey a e la ge han he o he pa icipa ing g oup. This
sugges s ha he applica ion o di e en ia ed esponsibili ies migh
be well accep ed by ich coun ies, which should be con i med by
mo e expe imen s and wo k ou side he lab. None heless, ou esul s
indica e ha pa icipan s beha iou can di e signi ican ly be ween
he e ogeneous and homogeneous sessions, which demons a es he
necessi y o in es iga e wha ac o s migh unde lie di e en esponses
o in o ma ion. Fu u e wo k migh also be able o un eil whe he
playe s om o he coun ies espond di e en ly o in o ma ion and
inequi y in a ge s.
One o he di icul ies o pe o ming synch onized expe imen s be-
ween wo coun ies, such as he ones p esen ed he e, is ob aining la ge
samples o mo e s a is ical powe . Despi e inding s a is ically signi i-
can e idence, ou es s a g oup le el ely on small samples, implying
cau ion while in e p e ing hese esul s. I emains open whe he
u u e eplica ions can ep oduce ou esul s wi h mo e g oups.

5
FRAMING & ALTRUISM
How sel ish so e e man may be supposed, he e a e e iden ly some
p inciples in his na u e, which in e es him in he o unes o
o he s, and ende hei happiness necessa y o him, hough he
de i es no hing om i , excep he pleasu e o seeing i .
Adam Smi h, Theo y o Mo al Sen imen s
Sea ed begga and
his dog,
Remb and
Policymake s, legisla o s, and public ins i u ions in gene al mus
know how people espond o incen i es and cons ain s. Fo qui e
some ime, a leas since Machia elli, i was belie ed ha humans
would always beha e sel ishly, hence public policy should aim a
p o iding ways o u n human sel ishness in o social wel a e
1
. This
jus i ied he widesp ead uses o ma e ial incen i es o mo i a e he
supposed homo economicus o ac in some speci ic way. Ne e heless, as
we ha e illus a ed in Sec ion 2.2, people ha e social p e e ences and
dis ega ding his ac can lead o subop imal policies [188], o e en
esul in public policy o back i ing [189]. “i is necessa y o
anyone who
o ganizes a epublic
and es ablishes laws
in i o ake o
g an ed ha all men
a e e il and ha hey
will always ac
acco ding o he
wickedness o hei
na u e whene e
hey ha e he
oppo uni y”
N. Machia elli
[190]
Incen i es seldom a e o hogonal and addi i e o people in insic
esponses, indeed, hey in e ac wi h hei mo al and psychological
mo i es, possibly inc easing hei p o-social esponse syne gis ically
o , on he con a y, unde mining i [12]. Ideally, he e o e, i is nec-
essa y o be awa e o he esul ing e ec o he incen i e, o , i no
possible, a leas obse e i i wo ks as in ended. Mo eo e , i also
should be aken in o accoun ha policies e icacy will also depend
on people’s imp ecise decision-making p ocess [191]. People beha e
acco ding o elusi e heu is ics [191–193] which doub ully will co -
espond o he beha iou o a sel -in e es ed and a ional agen . In
ac , humans demons a e p o-social esponses om an ea ly age,
which can be unde mined by ma e ial incen i es [4]. Mo eo e , he e
is widesp ead e idence ha people con ibu ions and in es men s
a e signi ican ly a ec ed by aming e ec s [191,194]. Thus, o de ise
e ec i e public policies and sus ainable business p ac ices i is impe -
a i e o ecognize humans’ na u al p opensi y o ac al uis ically [47]
and u he iden i y how people espond in each speci ic scena io. “i is ime o ully
emb ace wha I
would call
e idence-based
economics”
Richa d Thale
[33]
Na u ally, applying beha iou al expe imen s a e a sui able app oach
o enhance ou collec ion o people esponses in di e en scena ios.
I allows us o g asp how people a e expec ed o beha e wi hou he
bu den o he unin ended consequence o an ill-de ised policy. In his
1
Samuel Bowles p o ides a pi hy accoun o he o igin o his iew in [12]. In e es ingly,
he shows ha e en he p oponen s o he legisla ing o he sel ish man belie ed ha
humans had social p e e ences.
69
70 aming &al uism
ega d, socially esponsible in es men s and cha i able dona ions a e
pa icula ly ele an nowadays as global in e es in hem inc eases. To
unco e people’s esponses in hese wo con empo a y in es men si -
ua ions, we ha e pe o med wo expe imen s looking in how people’s
p o-sociali y can be a ec ed by he speci ics o i) public goods wi h
dona ions and ii) impac in es ing unds – in es men s whose goal
is o gene a e social and en i onmen al bene i s alongside economic
e u ns. In Sec ion 5.1and in Sec ion 5.2we p esen expe imen s o
unco e peoples’ choices in he i s and second cases, espec i ely.
5.1 aming e ec s in con ibu ions and dona ions 71
5.1 aming e ec s in con ibu ions and dona ions
F aming in mul iple goods games and dona ions o cha i ies,
unde e iew.
F. Maciel Ca doso, S. Meloni, C. G acia-Láza o, A.
An onioni, J. A. Cues a, Á. Sánchez, & Y. Mo eno
The numbe and economic ele ance o cha i ies and non-go e nmen al
o ganiza ions has apidly g own in he las ew decades. Fo ins ance,
mo e han 1.5million nonp o i s we e egis e ed wi h he US IRS
in 2015, con ibu ing a ound 5.4% o he US GDP [195]; in 2016/17,
he e we e 166,854 olun a y o ganiza ions in he UK, employing
abou 878 000 people [196]. This g ow h has been ueled by he subsi-
dies o many go e nmen s a ound he wo ld, ei he by ans e ing
unds di ec ly o o ganisa ions o h ough ax deduc ion policies o
dono s[197–204]. A he same ime, mo e han 1billion people gi e
money o cha i ies [205]. In iew o his olume o ac i i y, philan-
h opy and olun a y con ibu ions o cha i ies ha e a oused he
in e es o a g owing numbe o esea che s in he las decades [206,
207], leading o heo e ical models [208], quali a i e esea ch [209],
and expe imen al s udies on he economics o cha i y [210], und ais-
ing e en s [211], di e en o ms o und aising [212], and he e ec
o s a us [213], lead dono s [214], eba es [215], subsides [216], and
message aming [217] on cha i able gi ing.
Secondly, when s udying al uis ic beha iou in humans, gende
di e ences dese e special a en ion. Empi ical e idence sugges s ha
women gi e mo e o cha i ies han men [218]. Socio-cul u al and e o-
lu iona y heo ies p edic sex-di e en ia ed beha iou [219], al hough
hey o en disag ee on how men and women will beha e in speci ic
ci cums ances. Socio-cul u al heo y s esses he ole o cul u al s e eo-
ypes [220] whe eas e olu iona y heo y explains sex beha iou al
di e ences as adap a ions [221]. Pa icula ly, bo h heo ies ag ee on
he exis ence o beha iou al di e ences wi h espec o coope a ion
o al uism. Many expe imen s ha e been conduc ed o assess hese
di e ences, and in gene al, women show highe le els o coope a ion
and al uism han men [222–225], al hough o he s udies show ha
gende does no a ec hese ai s [226,227].
One o he mos equen ly used amewo ks o expe imen ally ad-
d ess dona ions o cha i ies is ha o public good games (PGG)[46].
The ep esen a ion o dona ions o cha i ies h ough a PGG is a
om pe ec , bu app oxima e enough o ha e been conside ed o en
in he li e a u e [228–230]. In his con ex , he esea ch ques ion we
add ess in his wo k ocuses on he e ec s o aming on bo h con i-
bu ions o PGGs and dona ions o cha i ies
2
. In o de o compa e he
2See [194] o a ecen e iew on aming in PGG.
72 aming &al uism
e ec i eness o di e en und aising schemes, we ha e ca ied ou an
expe imen in ol ing con ibu ing o mul iple PGG simul aneously.
In his ype o expe imen , subjec s can choose be ween wo o mo e
common po s o alloca e hei endowmen s, and he choices made by
hem a e used o assess he e ec s o di e en amings [231–234]. In
ou case, we ha e compa ed wo dis inc me hods o aising unds:
di ec e sus indi ec dona ions. To his end, we ha e de ised a special-
pu pose PGG wi h wo di e en ea men s: a i s se up in ol ing an
explici social ee, o ax (Di ec -Dona ion, hence o h DD), and ano he
one in ol ing an implici social ee (Indi ec -Dona ion, hence o h ID).
As we will see below, ou se up allowed us o simul aneously measu e
wo a iables: he con ibu ions o public goods and he amoun s
dona ed o cha i y. Rega ding hose dona ions, he e y exis ence o a
di ec sel -bene i p ecludes measu ing al uism, and, he e o e, we
ha e gi en he playe s he chance o con ibu e o se e al PGGs, which
di e ed in he ac ion o he bene i ha goes o cha i y. Fu he mo e,
he exis ence o unds wi h di e en social axes enables us o s udy
he pa e n o con ibu ions and hei co esponding aming e ec .
Ou expe imen p o ides se e al ele an conclusions conce ning
how people espond o amings in ending o inc ease con ibu ions
wi h a social impac channeled h ough cha i ies. We ha e obse ed
ha aming a ec s he choice o con ibu ions depending on he
dona ion s uc u e: Indi ec dona ions led o g ea e o al con ibu ions
han social axes. Con e sely, he e was no in luence o aming on
dona ions o cha i y: he ac ion o he con ibu ions de o ed o
cha i y is no a ec ed by how hose dona ions a e p esen ed, i.e., as
indi ec o as di ec dona ions. Rega ding gende in luence, we ha e
ound ha women con ibu e o public goods and dona e o cha i y
mo e han men. All hese indings may ha e implica ions o in e es
o he design o socially esponsible in es ing s a egies.
5.1.1Expe imen al design
Figu e 5.1shows a schema ic ep esen a ion o he expe imen al se up.
Expe imen s we e conduc ed on g oups o 10 pa icipan s. Each g oup
played an i e a ed PGG wi h 5 unds, which di e ed in he ac ion o
p o i dona ed o cha i y (0%, 5%, 10%, 15%, 20%, espec i ely). In a
s anda d PGG, pa icipan s con ibu e o a common po , and he o al
o he po is mul iplied by he so-called mul iplica ion ac o , being
subsequen ly equally dis ibu ed among all pa icipan s i espec i e
o hei con ibu ion. In e e y ound, subjec s we e gi en 100 expe -
imen al cu ency uni s (he ea e , ECU) which hey could dis ibu e
among he i e unds a will.
A guably, he e a e wo na u al app oaches o implemen dona ions
in a PGG scena io: dona ions coming om axes on he con ibu ions
o coming om dec eases in he p o i abili y. To s udy he e ec s
5.1 aming e ec s in con ibu ions and dona ions 79
FFC
FKP
DD ID DD ID
0
5
10
15
F aming
To al Dona ion
Di ec Dona ion
Indi ec Dona ion
A
FFC
FKP
1 5 10 15 20 1 5 10 15 20
5
10
Round Numbe
To al Dona ion
B
Figu e 5.3:To al dona ions o cha i y in he FC phase. A)
Boxplo o he
a e age o al dona ion by subjec du ing he cou se o he expe -
imen . The lowe and uppe hinges co espond o he i s and
hi d qua iles. The uppe ( esp. lowe ) whiske ex ends om he
hinge o he la ges ( esp. smalles ) alue no u he han 1.5* IQR
om he hinge.
B)
G oup a e ages a each ound. The shaded
a ea co esponds o 0.95 boo s apped con idence in e al.
Di =β0+β1IDi+ui (M4)
Di =β0+β1IDi+β2FKPi+β3IDi∗FKPi+ui (M5)
Di =β0+β1IDi+β2FKPi+β3IDi∗FKPi+β4Wi+ui (M6)
The analysis con i ms ha , ega ding dona ions o cha i y, he e is
nei he di e ence be ween ea men s no o de e ec s. None heless,
women dona e signi ican ly mo e (i.e., con ibu e o unds wi h highe
dona ion a e) han men.
5.1.2.3Dis ibu ion o con ibu ions
The expe imen was designed wi h i e di e en unds wi h di e en
social axes o allow us o s udy he pa e n o con ibu ions and he
e ec s o aming on i . Besides, in he case o a aming e ec , being
able o ex ac a pa e n in he con ibu ions can help us o in es iga e
he possible d i e s behind he di e ences be ween he wo amings.
To s udy he dis ibu ion o con ibu ions in he i e di e en unds,
we ha e ca ied ou eg ession analyses o he con ibu ions in bo h FC
and KP phases. We pe o med indi idual eg essions o check whe he

80 aming &al uism
Dependen a iable:
To al Dona ion
(4) (5) (6)
Indi ec Dona ion 0.198 0.548 0.549
(0.803) (1.002) (0.963)
FKP −0.273 −0.010
(1.129) (1.013)
Women 3.943∗∗∗
(0.772)
Indi ec Dona ion x FKP −0.700 −0.701
(1.601) (1.438)
Cons an 7.446∗∗∗ 7.583∗∗∗ 5.086∗∗∗
(0.565) (0.660) (0.778)
Obse a ions 2,347 2,347 2,347
R20.0004 0.005 0.139
Adjus ed R2−0.0001 0.003 0.138
F S a is ic 0.546 10.542∗∗ 379.479∗∗∗
No e: ∗p<0.1;∗∗p<0.05;∗∗∗p<0.01
Table 5.3:Reg ession esul s o he dona ions o cha i y.
Random-e ec s
(Wallace and Hussain es ima o ) wi h clus e obus s anda d e o s
a he indi idual le el. Column (4) e e s o he model o subjec s’
dona ions wi h DD as he e e ence (Equa ion M4). In (5), wo
e ms ha e been added o (4): he FKP e m aking in o accoun he
o de , plus an addi ional e m o he in e ac ion be ween he o de
and he ea men , being DD
×
FFC he e e ence (Equa ion M5).
Column (6) e e s o he model (5) plus a W e m o he gende ,
being a male subjec playing DD
×
FFC he e e ence (Equa ion
M6).
5.1 aming e ec s in con ibu ions and dona ions 81
he a iables’ e ec s on con ibu ions a ied ac oss unds in he wo
ea men s. Equa ion M7desc ibes he eg ession o und
, whe e
he dependen a iable
Ci
co esponds o he amoun con ibu ed
by subjec
i
, a ime
o he und
. No e ha a di e en eg ession
has been pe o med o each und in a gi en phase. Resul s o he
eg essions o he FC ( esp., KP) phases a e shown in able 5.4( esp.,
5.5).
Ci =β0+β1IDi+β2FKPi+β3IDi∗FKPi+β4Wi+ui (M7)
Table 5.4shows he esul s o he FC phase, whe ein pa icipan s
could only decide how o dis ibu e hei con ibu ions. As shown,
pa icipan s om di e en ea men s seem o con ibu e in a simila
ashion when unds a e conside ed in isola ion. The only signi ican
e ec is obse ed o gende , women being mo e likely o con ibu e a
la ge sha e o unds wi h a posi i e social ax while con ibu ing less
o he und wi h no social ax. Thus, hey end up dona ing o cha i y
mo e han men.
Table 5.5displays he esul o he same eg essions o he KP
phase, whe ein pa icipan s can decide he amoun hey con ibu e o
public goods. Clea ly, women also dona e o cha i y mo e han men
in his phase, as hey a e mo e likely o choose unds wi h a highe
social ax. The e is a highe con ibu ion associa ed wi h pa icipan s
playing he ID ea men in he FFC, none heless, his was expec ed as
pa icipan s con ibu ed mo e in o al as shown in p e ious sec ions.
Summa izing, di e ences in indi idual unds con ibu ions a e a
consequence o ou p e ious indings. Speci ically, being a woman
o playing he ID ea men in o de FFC is associa ed wi h highe
con ibu ions.
5.1.3Discussion
In o de o explain he obse ed di e ences in con ibu ions be ween
he wo ames, as well as he obse ed gende di e ences, we ha e
s udied hei possible causes. On he one hand, we ha e pe o med
eg ession analyses o e alua e possible di e ences be ween ea men s
wi h espec o he esponses o subjec s o he beha iou o he es
o he playe s in hei g oup, as well as di e ences in he condi ional
con ibu ion be ween gende s. The de ails o hese analyses can be
ound in Sec ion c.1o he Appendix. Reg ession esul s indica e
ha pa icipan s do no condi ion hei con ibu ion o o he playe s’
beha iou . The e is nei he e idence ha men o women would eac
di e en ly o his gene al end, no signi ican di e ences be ween
di e en amings in his espec .
A plausible explana ion o he obse ed in luence o aming on
con ibu ions should lie in how in o ma ion is p esen ed o he playe s.
82 aming &al uism
Dependen a iable: Ci
0 5%10%15%20%
ID −3.774 3.521 −3.229 0.047 3.439
(7.048) (3.343) (2.418) (2.339) (3.052)
FKP 2.813 −1.925 −3.435 1.632 0.910
(7.122) (1.928) (2.438) (3.641) (3.585)
Women −25.784∗∗∗ 2.738 5.441∗∗∗ 5.199∗∗ 12.411∗∗∗
(5.744) (2.545) (1.774) (2.428) (2.358)
ID x FKP 1.132 1.236 4.611 −3.437 −3.529
(10.292) (4.389) (3.175) (4.400) (4.677)
Cons an 58.036∗∗∗ 11.673∗∗∗ 10.405∗∗∗ 10.228∗∗∗ 9.642∗∗∗
(6.121) (2.154) (2.584) (2.020) (2.541)
Obse a ions 2,347 2,347 2,347 2,347 2,347
R20.133 0.021 0.047 0.029 0.095
Adjus ed R20.131 0.020 0.045 0.027 0.093
F S a is ic 358.453∗∗∗ 51.261∗∗∗ 115.645∗∗∗ 70.157∗∗∗ 245.595∗∗∗
No e: ∗p<0.1;∗∗p<0.05;∗∗∗p<0.01
Table 5.4:Random E ec s eg ession wi h clus e obus s anda d e o s
a he indi idual le el o he Fo ced Con ibu ion phase.
Each
column co esponds o a und o a de e mined social ax, namely:
0,5%, 10%, 15%, 20%, om le o igh . The e e ence is a male
subjec playing DD×FFC.
5.1 aming e ec s in con ibu ions and dona ions 83
Dependen a iable: Ci
0 5%10%15%20%
ID −3.948 0.812 −2.066 −2.292 5.839∗
(5.711) (1.646) (1.776) (1.882) (3.079)
FKP 0.017 2.295 0.857 0.846 4.434
(5.480) (1.571) (1.716) (1.764) (3.196)
Women −11.060∗∗ 4.103∗∗ 4.643∗∗∗ 5.156∗∗∗ 9.336∗∗∗
(4.718) (1.778) (1.256) (1.377) (2.275)
ID x FKP 11.976 5.853∗4.935∗∗ 5.068∗−6.757
(8.265) (3.366) (2.474) (2.658) (4.570)
Cons an 31.870∗∗∗ 4.616∗∗∗ 5.227∗∗∗ 5.906∗∗∗ 6.479∗∗∗
(5.665) (1.414) (1.350) (1.639) (2.050)
Obse a ions 2,363 2,363 2,363 2,363 2,363
R20.057 0.077 0.065 0.063 0.070
Adjus ed R20.056 0.076 0.063 0.061 0.069
F S a is ic 143.432∗∗∗ 197.424∗∗∗ 162.838∗∗∗ 157.617∗∗∗ 178.595∗∗∗
No e: ∗p<0.1;∗∗p<0.05;∗∗∗p<0.01
Table 5.5:Random E ec s eg ession wi h clus e obus s anda d e o s
a he indi idual le el o he Keep in he Pocke phase.
Each
column co esponds o a und o a de e mined social ax, namely:
0,5%, 10%, 15%, 20%, om le o igh .
84 aming &al uism
In his ega d, axes a e only shown o pa icipan s playing he DD
ea men , being he p esence o axes he main di e ence be ween
he wo ea men s. Acco ding o his explana ion, ID playe s eac
nega i ely o he ax while con ibu ing. Con e sely, DD playe s a e
no be a ec ed by he educ ion in he p o i abili y o he same deg ee.
Fu he mo e, he ac ha he aming e ec is obse ed only in he
FKP o de sugges s ha subjec s ha play i s he FC phase a e
condi ioned by his lea ning e ec , being hei con ibu ions in he
subsequen KP phase independen o he aming.
5.1.3.1Conclusions
Summa ising ou esul s, by using a se up based on a PGG modi ied o
include a social esponsibili y ac o , we ha e ound ha aming will
a ec und con ibu ions depending on how he dona ion p ocedu e
is implemen ed. On he one hand, con ibu ions a e highe when he
associa ed social dona ions a e p esen ed as indi ec dona ions han
as social axes. On he o he hand, he ac ion o he con ibu ions
de o ed o cha i y is no a ec ed by he aming e ec . This esul
is no un ela ed o he wo k o K ieg and Samek [234], whe e hey
obse e ha a e u n o a 20% o he con ibu ion back o he dono
inc eases signi ican ly he con ibu ion le el, whe eas ecogni ion
o sanc ions ha e no e ec . We ha e also ound ha , on a e age,
women con ibu e o he public goods and dona e o cha i y mo e
han men, which is obse ed in some philan h opy con ex s [235].
The implica ions o hese indings a e c ucial o policy-make s in he
design o socially esponsible in es ing s a egies and ai policies,
e.g., when he go e nmen o a cha i y in ends o p omo e socially
esponsible conduc s, o compe e success ully o he limi ed amoun
o unds a ailable o he di e en cha i ies. People a e no only sel -
in e es ed, none heless, bu hei likelihood o ac ing p osocially can
also be in luenced by he ype o incen i e and economic con ex [12].
In his ega d, he esul s o Co azzini e al. [233] poin o he ele ance
o a oiding miscoo dina ion among dono s by making pa icula
op ions salien . The mechanism we ha e iden i ied he e could hen be
one op ion o p o ide such saliency.

5.2 unde s anding d i e s when in es ing o impac 85
5.2 unde s anding d i e s when in es ing o impac
Unde s anding d i e s when in es ing o impac : an
expe imen al s udy [236].
L. De Amicis, S. Binen i, F. Maciel Ca doso, C.
G acia-Láza o, A. Sánchez, & Y. Mo eno
In ecen yea s, impac in es ing has isen o p ominence in a global
business en i onmen ha is inc easingly conce ned, and a imes e en
p essu ed, o ake in o accoun social and en i onmen al issues. Impac
in es ing is hus ma king a new end among adi ional p ac i ione s,
ins i u ions and policymake s wo ldwide, and he ange o impac
in es men op ions and oppo uni ies a global le el has na u ally
g own in pa allel o he expanding in e es in social in es men . The
Global Impac In es ing Ne wo k [237] es ima es ha he sec o has
g own om $4.3billion in 2011 o $502 billion in 2018
3
and, a he
uppe end o he ma ke , impac in es ing is es ima ed o each as
much as $1 illion in alue by 2020 [238].
In ligh o his new end, a g owing body o esea ch eme ged
o de ine he heo y and p ac ice o social inance. The GIIN [239]
de ines impac in es men s as a o m o in es men ha is “made in o
companies, o ganisa ions, and unds wi h he in en ion o gene a e
social and en i onmen al impac alongside a inancial e u n”. Ac-
co ding o his in e p e a ion o he e m and phenomenon - a guably
he mos acc edi ed and quo ed one - he wo de ining elemen s o
impac in es men s a e he expec a ion o inancial e u ns on capi-
al, o a minimum a e u n o capi al, and in en ionali y, namely he
in en ion o ha ing a posi i e impac as a di ec consequence o a
delibe a e ac ion. Despi e he cen ali y o expec a ions and in en ion-
ali y, cu en esea ch has mainly ocused on impac assessmen and
measu emen amewo ks aimed a cap u ing he en i onmen al and
social e u ns gene a ed by in es men s ([240], [241]; [242], [243–249]
). While such a ocus is c i ically impo an o ma e s o e ec i e-
ness, accoun abili y and anspa ency, i ep esen s a deba ed and
con es ed ield ha domina es and la gely monopolise esea ch on
social in es men s. Compa ed o o he ins ances o socially esponsible
business p ac ices ha ha e been widely in es iga ed h ough he lens
o epu a ion/b and building and consump ion heo ies ([250], [251],
[252]), li le esea ch has been conduc ed on he socio-demog aphic
cha ac e is ics and he beha iou al d i e s pushing in es o s o choose
impac unds o e adi ional in es men s.
Ye , i we a e o make social inance a “s anda d p ac ice”, i is c ucial
o look a wha migh ende impac -o ien ed unds a mo e appealing
in es men op ions and o whom – in his ligh , his s udy aims o con-
3
The es ima e is based on he esponses p o ided by 266 leading impac in es ing
o ganiza ions om a ound he wo ld, managing collec i ely $239 billion.
86 aming &al uism
ibu e o his esea ch gap h ough an expe imen -based in es iga ion.
The alue o explo ing in es o s’ beha iou and hei decision-making
p ocess is wo- old. Fi s , in he con ex o beha iou al economics
and game heo y, such a ocus can add signi ican alue o exis ing
esea ch by shedding ligh on he nudging ac o s and de e minan s
in luencing he choices o economic ac o s (i.e., in insic alue o he
esea ch ocus). Second, beha iou al insigh s can ha e implica ions
o no ma i e ini ia i es o incen i e ac ions aimed a pushing he
impac in es ing end in o he mains eam, such as awa eness- aising
campaigns, ma ke ing s a egies and policy-making (i.e., ins umen al
alue o he esea ch).
Wi hin his wide scope o in es iga ion and ocus, he p esen
expe imen -based esea ch aims o add ess he ollowing ques ions:
RQ1
Wha is he e ec o p e ious knowledge abou impac in es ing?
Do economic ac o s in es di e en ly i hey a e al eady amilia
wi h he concep o impac in es ing as opposed o hose who
ha e ne e hea d o i ?
RQ2
How do in es o s’ p e e ences change depending on he way
di e en in es men ins umen s a e p oposed o hem?
RQ3
How much inancial e u n a e in es o s willing o sac i ice o
social impac , conside ing di e en isk ac o s?
RQ4
Do ex e nal ac o s a ec he beha iou o economic ac o s
(i.e., could incen i es om he go e nmen change in es o s’
beha iou )?
The expe imen consis s o a mul iple-choice game en isaging di -
e en in es men scena ios. Acco ding o hei pe o mance in an
e o ask a he beginning o he game, pa icipan s a e gi en a
budge o simula e in es men decisions unde di e en incen i e
ci cums ances while con olling o di e en a iables, such as p io
knowledge abou impac in es ing. The expe imen is di ec ed a wo
di e en sample g oups: non-expe s, who a e likely o ha e no p io
knowledge on he concep o impac in es ing, and “expe s”, namely
p o essionals wo king in he impac in es ing sec o . As an incen i e
o elici u h ul beha iou , and a a iance wi h adi ional su eys,
pa icipan s a e economically ewa ded acco ding o he ea nings hey
make h ough hei in es men decisions. Following he expe imen ,
he da a is analysed h ough logis ic eg essions. This app oach was
p e e ed o e pe cen ages as he eg ession analysis allowed o isola e
he e ec o each a iable.
The esea ch design allows o d aw a numbe o conclusions ha
will be o in e es o s akeholde s and policy-make s aiming o p o-
mo e impac in es ing. The s udy concludes ha people ope a ing
in he sec o (expe s) and emale pa icipan s end o a ou he im-
pac in es ing op ion. Fu he mo e, he olde people a e, he mo e
5.2 unde s anding d i e s when in es ing o impac 87
Non-expe s Expe s
Female Male Female Male
3-yea Bachelo 33 14 1 1
4-yea Bachelo 79 45 2 4
5-yea Bachelo 59 24 2 3
Lowe seconda y educa ion 15 10 0 0
Mas e (1yea ) 35 20 4 7
Mas e (2yea s) 31 15 11 11
O he (non-lis ed) 20 7 2 0
PhD 7 4 3 8
Pos -seconda y, non- e ia y ed. 18 20 0 0
Sho -cycle, e ia y educa ion 21 18 0 1
Uppe seconda y educa ion 23 23 1 0
To al 341 200 26 35
Table 5.6:Pa icipan s’ le el o educa ion
. Le el o o mal educa ion o
Non-Expe s ( wo le mos columns) and Expe s ( wo igh mos
columns).
a ac ed o impac in es ing hey appea o be. Ex e nal ac o s such
as iscal incen i es in luence posi i ely, al hough only ma ginally, he
esponden s’ beha iou in choosing Impac In es ing Funds (IIF) o e
T adi ional In es ing Funds (TIF). No clea co ela ion has been ound
be ween he pa icipan s’ educa ional le el and hei disposi ion o
in es o impac . P o iding addi ional de ails o , mo e e ec i ely,
images on he social pu pose and impac o he IIF has p o ed o
be c i ical in subs an ially inc easing he p obabili y o op ing o an
IIF o e a TIF, bo h o male and emale pa icipan s. Fu he mo e,
pa icipan s we e less likely o choose he IIF op ion when his was
associa ed wi h highe isk ( o bo h male and emale pa icipan s).
Finally, when conside ing pa icipan s’ p io knowledge on he opic,
he di e ence be ween con ol g oups was ela i ely small - ye , i
appea s ha p o iding pa icipan s wi h key in o ma ion on social
inance (by showing hem a ideo) had a posi i e impac wi h no ma-
i e implica ions o cu en incen i e s uc u es, awa eness campaigns
and educa ional p og ammes abou impac in es ing.
88 aming &al uism
Non-expe s Expe s
Female Male Female Male
A gen ina 7 1 0 0
I aly 0 0 7 11
Aus alia 1 0 1 0
Luxembou g 0 0 1 0
Aus ia 0 0 1 1
Mexico 8 4 0 0
Belgium 1 1 0 0
Ne he lands 0 0 2 1
Boli ia 0 1 1 1
Pa aguay 1 0 0 0
B azil 1 0 0 0
Pe u 1 1 0 0
Chile 10 1 0 0
Poland 0 0 1 0
Colombia 7 7 0 0
Po ugal 2 2 0 0
C. Rica 0 1 0 0
Russia 0 1 0 0
C oa ia 1 0 0 1
Se bia 0 0 0 1
Ecuado 0 2 0 0
Spain 282 166 0 2
El Sal ado 1 0 0 0
Swi ze land 0 0 1 3
F ance 0 2 2 1
Tunisia 0 0 1 0
F ance+ 1 0 0 0
U.K. 1 2 7 11
Geo gia 1 0 0 0
U.S.A. 2 0 0 0
G eece 0 1 0 1
U uguay 3 1 0 0
Hunga y 0 0 1 0
Venezuela 9 5 0 0
I eland 1 0 0 1
Zambia 0 1 0 0
Table 5.7:Coun y o Residence o pa icipan s.
F ance+ s ands o O e -
seas F ance.
5.2 unde s anding d i e s when in es ing o impac 95
TIF s IIF Impac Desc ip ion Risk Fac o
In e cep 1.05 (0.02)∗∗∗ 1.08 (0.02)∗∗∗ 0.91 (0.02)∗∗∗
Mul iple Ques ion −0.03 (0.02)−0.01 (0.02)0.04 (0.02)
Del a −0.20 (0.01)∗∗∗ −0.19 (0.01)∗∗∗ −0.16 (0.01)∗∗∗
AIC 3481.80 3270.87 3843.07
BIC 3505.83 3294.91 3867.11
Log likelihood -1736.90 -1631.44 -1917.53
De iance 558.86 521.04 630.13
Num. obs. 3010 3010 3010
∗∗∗p<0.001, ∗∗p<0.01, ∗p<0.05
Table 5.11:F aming o mul iple ques ions and und p o i abili y.
Log-odds
a io o coe icien s ob ained by logis ic eg ession. Each column
co esponds o a di e en eg ession analysis: TIF s IIF (Q1and
Q2), impac desc ip ion (Q3and Q4), and isk ac o (Q5and
Q6). The in e cep co esponds o he log-odds a io which chose
he IIF o e he TIF (Q1, Q3, Q5). Mul iple Ques ion coe icien s
co espond o he di e ence in e ec when p oposing di e en
op ions (Q2, Q4, Q6) wi h espec o he in e cep (Q1, Q3, Q5,
espec i ely). Del a coe icien s accoun o e ec IIFs e u n (Q2,
Q4, Q6), i.e., hey e e o he e u n di e ences be ween TIF and
IIF. Obse a ions co espond o all pa icipan s’ esponses o he
wo-choice ques ions and hei co esponding mul iple ques ion
(Q1and Q2, Q3and Q4, Q5and Q6).
Age also a ec s esponses dis inc i ely in each ques ion, as we discuss
u he in he nex pa ag aphs.
The i s column o Table 5.12 shows ha : i) Women a e mo e likely
o in es in an IIF han men (
p<0.001
), ii) expe s a e mo e likely o
in es in an IIF han non-expe s (
p<0.001
), and iii) he willingness
o in es in IIF inc eases wi h age (
p<0.001
). On he o he hand, he
educa ion le el does no make a subs an ial di e ence in explaining
he beha iou o in es o s. Fu he mo e, al hough p e ious knowledge
on impac in es ing (acco ding o he sel -assessmen o pa icipan s)
does no in luence he in es men decision, he in o ma i e ideo
played a posi i e ole: pa icipan s who we e shown a u o ial ideo
on impac in es ing displayed a highe endency o in es in IIF han
hose who did no wa ch i (p<0.001).
When addi ional in o ma ion on he ac ual impac achie ed by he
IIF was gi en o pa icipan s (second column o Table 5.12) i) gende
di e ences pe sis , wi h women being mo e likely o in es in IIFs han
men (
p<0.001
), ii) expe s a e also mo e likely o in es in IIFs han
non-expe s (
p<0.001
). Con e sely, nei he age no educa ion has a
signi ican in luence on IIF in es men choices. No e ha , al hough
wi hou addi ional in o ma ion on social impac IIF in es men s in-
c ease wi h age ( i s column eg ession), his de e minan disappea s
when addi ional in o ma ion is p o ided (second column).

96 aming &al uism
The e ec s o associa ing a highe isk wi h he IIF op ion (20%
chance o no yielding a e u n wi h IIF e sus a 10% chance wi h
TIF) a e shown on he hi d column o Table 5.12. I is shown ha : i)
Women a e mo e likely o in es in highe isk IIF op ions han men
(
p<0.001
), ii) op ing o highe isk IIF inc eases wi h age (
p<0.001
).
On he o he hand, when a highe isk is associa ed wi h he IIF, he
highe endency o expe s o in es in IIFs anishes.
Rega ding ax deduc ions ( ou h column o Table 5.12), su p isingly,
a signi ican e ec o ax deduc ions on he impac in es ing op ion
was no ound, excep o expe s and olde subjec s, who display
a posi i e esponse o ax bene i s. I is obse ed ha , when a ax
incen i e is included in he scena io, expe s (
p<0.05
) and olde
subjec s (
p<0.01
) show a highe endency o in es in IIFs. As in
p e ious cases, al hough p io knowledge on impac in es ing does no
show a signi ican in luence on impac in es ing choices, pa icipan s
who wa ched he in o ma i e ideo showed a highe endency o
in es in IIFs han hose who did no see i (
p<0.001
). This endency
is s onge when a ax deduc ion is included.
Finally, ega ding he e ec o an addi ional isual incen i e, he
ou h column o Table 5.12 shows he logis ic eg ession o he
scena io in which addi ional de ails on social impac suppo ed by an
image we e showed o pa icipan s. As explained be o e, he isual
aid has a signi ican posi i e in luence op ing o IIFs. In his scena io,
gende is he only demog aphic a iable ha plays a signi ican ole
in he willingness o in es in IIFs - women showed we e mo e likely
o op o IIFs o e TIFs (
p<0.01
). Nei he expe ise, age, educa ion
le el, p io knowledge showed a signi ican in luence on in es men
choices. Al hough women display a highe p obabili y o op o IIFs
han men in he p esence o a isual incen i e, i canno be s a ed ha
isual aids a ec mo e women han men, since he di e ence in i s
in luence is no signi ican acco ding o logis ic eg ession.
5.2.3Discussion
Ou esul s indica e ha in mos scena ios expe s a e mo e likely han
non-expe s o choose he impac in es men op ion. This does no
eally come as a su p ise: i is likely ha expe s en e ed he impac
in es ing ield d i en by pe sonal p inciples and mo al conside a ions
[259,260], as wo king in he wo ld o social inance may al eady e lec
pe sonal comp omises be ween a less luc a i e ca ee and an e hical
p o essional pa h[261,262].
Ou indings show ha olde people ha e a highe endency o
choose impac in es men op ions han younge people. This is some-
wha su p ising gi en he cu en momen um o na a i es such as
“Millennials Will B ing Impac In es ing Mains eam” [263], whe eby
young gene a ions a e expec ed o shi la ge capi als owa ds social
5.2 unde s anding d i e s when in es ing o impac 97
TIF s IIF Impac Desc. Risk Fac o Tax Ded. Visual Aid
In e cep 2.09∗∗∗ 2.87∗∗∗ 1.49∗∗∗ −0.17 2.38∗∗∗
(0.20) (0.22) (0.19) (0.48) (0.64)
Male −0.47∗∗∗ −0.50∗∗∗ −0.65∗∗∗ 0.11 −0.78∗∗
(0.09) (0.09) (0.09) (0.23) (0.30)
Expe 0.74∗∗∗ 0.65∗∗∗ 0.34 2.23∗1.76
(0.19) (0.20) (0.18) (1.05) (1.09)
Age 0.02∗∗∗ 0.01 0.02∗∗∗ 0.04∗∗ 0.01
(0.00) (0.00) (0.00) (0.01) (0.01)
H.Ed. −0.11 −0.16 −0.25∗−0.15 −0.06
(0.12) (0.12) (0.11) (0.29) (0.38)
P.Ed. 0.05 0.24 0.11 0.20 0.35
(0.14) (0.14) (0.13) (0.36) (0.50)
O he 0.31 0.20 0.38 0.30 −0.29
(0.23) (0.24) (0.22) (0.61) (0.70)
P.K. 0.15 0.06 0.06 0.22 −0.17
(0.12) (0.12) (0.11) (0.28) (0.39)
V. Disp. 0.35∗∗∗ 0.27∗0.27∗∗ 0.98∗∗∗ 0.00
(0.10) (0.10) (0.10) (0.26) (0.34)
Del a −0.97∗∗∗ −0.96∗∗∗ −0.71∗∗∗
(0.04) (0.04) (0.04)
AIC 3262.16 3084.17 3545.96 551.29 352.44
BIC 3322.26 3144.27 3606.06 590.89 392.04
Log Likelihood -1621.08 -1532.08 -1762.98 -266.64 -167.22
De iance 3242.16 3064.17 3525.96 533.29 334.44
Num. obs. 3010 3010 3010 602 602
∗∗∗p<0.001, ∗∗p<0.01, ∗p<0.05
Table 5.12:Demog aphic a iables impac .
Each model (column) co e-
sponds o a eg ession o each aming ype. TIF s IIF conside s
da a om Q1and Q2;Impac Desc., Impac Desc ip ion om Q3
and Q4;Risk Fac o om Q5and Q6;Tax Ded., Tax deduc ion om
Q7;Visual aid om Q8. We conside h ee h ee di e en le els o
educa ion: highe educa ion (H. Ed.), pos g adua e educa ion (P.Ed.),
and o he (i.e., non-cu icula educa ion besides basic educa ion
p og ams). P.K. is a dummy con olling o p e ious knowledge
abou impac in es ing and V. Disp. (Video displayed) is a dummy
indica ing i pa icipan s ha e wa ched he ideo. Del a coe i-
cien s co espond o he e u n di e ences be ween TIF and IIF.
Obse a ions co espond o all pa icipan s’ esponses o ques-
ions acco ding o he aming ype, columns om le o igh :
Q1and Q2, Q3and Q4, Q5and Q6, Q7, and Q8.
causes, as well as p io i ising socially meaning ul ca ee s and hus
ocus on social en ep eneu ship [264,265]. Ne e heless, some s ud-
ies ha e also shown ha senio ci izens a e mo e p one o con ibu e
o he common good [266], due o hei willingness o lea e a pos-
i i e legacy behind. The explana ion o such a esul may be ha
98 aming &al uism
he younge gene a ions a e in e es ed in impac in es men bu do
no ha e enough expe ise o do no eel con iden enough o ake
pa in i . Indeed, he Financial Times [267] epo s ha “while 64%
o he younge gene a ion C edi Suisse su eyed we e in e es ed in
impac in es ing, only 24% had ac ually in es ed”. Numbe s e en
dec ease when looking a high ne wo h amilies. A esea ch om
Mo gan S anley [268] shows ha only 4% o Nex Gen amily membe s
conside hemsel es ully-ac i e pa icipan s spending “a g ea deal”
o ime engaged in impac in es ing, al hough he majo i y (60%) o
Nex Gens conside “impo an ” o use hei amily’s weal h o make
a posi i e social o en i onmen al impac .
Fo almos all he ques ions, we can obse e ha women a e also
mo e willing o choose an IIF han men, excep o he ax educ ion
ques ion. This is well in line wi h he abundan li e a u e on philan-
h opy and cha i y-gi ing ha shows ha women a e mo e likely
o engage in al uis ic beha iou [235,269]. E en when a isk ac o
is in oduced, mo e women p e e an IIF compa ed o male pa ici-
pan s despi e hey a e gene ally conside ed o exhibi a isk-a e se
beha iou . The endency o women o p e e an IIF o e a TIF is in
line wi h exis ing esea ch om he indus y. S ephanie Luedke o
Ci i In es men Managemen , who wo ks on he on lines o asse
alloca ion, con i med in a ecen in e iew on Fo bes [270] ha “90%
o women su eyed ha e indica ed ha hey wan o in es a leas
a po ion o hei weal h in a manne ha aligns wi h hei alues”.
On he op o ha , women a e becoming weal hie , hanks o a mo e
gende -equal in e gene a ional ans e o weal h [271], and a e p o -
ing o ha e en e ed a adi ionally "male" en i onmen as capable
in es o s, as showed in a esea ch om Fideli y in which women
ended o ou pe o m men in gene a ing a e u n on hei in es men s
[272].
When conside ing pa icipan s’ p io knowledge on he opic, lea -
ing expe ise on he side, he di e ence be ween con ol g oups is no
signi ican . Ye , he expe imen e eals ha showing he ideo had
a posi i e impac in p omp ing socially o ien ed decisions, whe eby
signalling a wide scope o p omo ing and aising awa eness abou
impac in es ing. This is con i med by ou logis ic eg essions and
ep esen s one o he mos impo an indings o ou esea ch in line
wi h ecen s udies on he same opic [265]. Public adminis a ion bod-
ies and ci il socie y o ganisa ions ha e al eady s a ed o pu e o s
in aising awa eness abou impac in es men . O ganisa ions such
as Big Socie y Capi al, he social in es men “wholesale ” se up in
2012 by Da id Came on oge he wi h his Big Socie y agenda, o he
Social Impac Agenda p omo ed by he Po uguese Go e nmen a e an
example o his. In e na ional poli ical bodies, such as he Eu opean
Union, did no adop a “wai and see” app oach; on he con a y,
hey ook signi ican , ac i e s eps o wa d, such as he c ea ion o
5.2 unde s anding d i e s when in es ing o impac 99
he Expe G oup on Social En ep eneu ship (GECES) in 2011 and
he consequen epo in 2016 – “Social En e p ises and Social Econ-
omy going o wa d” [273] – ad oca ing o a g ea e isibili y and
enhanced unde s anding o social en e p ises and impac in es men s.
This kind o ini ia i es, howe e , gene a ed mixed esul s; mo e needs
o be done no only by coo dina ing e o s be ween go e nmen s and
in e na ional ins i u ions bu also by encou aging in e -sec o ial collab-
o a ions be ween esea che s, he p i a e sec o and p ac i ione s om
he social economy and he social en e p ise wo ld, who could wo k
oge he o ga he s onge e idence on he added alue o impac
in es men and be e communica e hei main esul s h ough ins i u-
ional channels. In his ega d, media ou le s a e cu en ly missing an
oppo uni y, especially in ligh o he posi i e gene al a i ude owa ds
he opic in public na a i es [265]. Fu he mo e, impac in es ing is
no cu en ly pa o he cu iculum o inance deg ees and is no pa
o he o mal aining o a inancie o co po a e in es o . Top uni e -
si ies a e aking new s eps in making inno a i e inance pa o he
mains eam and a e inc easingly engaged in he impac in es ing de-
ba e, knowledge-sha ing and aining. Fo ins ance, he Said Business
School a he Uni e si y o Ox o d has ecen ly launched a p og amme
en i led “Ox o d Impac In es ing P og amme: Build you in es men
skills o deli e maximum social e u n”, di ec ed a p o essionals
and businesses ha aim o en e he ield - his in eg a es he wo k
al eady unde ook by he Skoll Cen e o Social En ep eneu ship. In
he same way, he Camb idge Ins i u e o Sus ainabili y Leade ship
(CISL) g ea ly ocuses on sus ainable business and leade ship. Ye ,
hese s anda n uni e si y deg ees ha dly co e impac in es ing. As
a esul , whils uni e si ies a e inc easingly ea ing opics ela ed o
managemen and inno a ion o social good, he e is s ill a long way o
go in shi ing he way we app oach mains eam inancial aining and
educa ion, which could be a g ea s a ing poin o adically change
mains eam inance.
Ano he e lec ion poin is abou ax incen i es, usually seen as
a s ong ma ke builde . In ou expe imen , he ax incen i e is he
only case in which gende does no play a signi ican ole, and bo h
men and women do no see i as an incen i e. This was a somewha
su p ising, key inding o ou esea ch. As a ma e o ac , despi e
wha academic e idence sugges s and ou expe imen con i ms, public
bodies s ill pu a g ea emphasis on he ax bene i s o gi ing. The UK
Go e nmen , o ins ance, has in oduced he Social In es men Tax
Relie (SITR) scheme in 2014 - ye , he esul s ha e no been as posi i e
as expec ed. In 2016-17,25 social en e p ises ecei ed new in es men s
h ough he SITR scheme and £1.8million o unds we e aised. Since
SITR was launched in 2014-15,50 social en e p ises aised unds o
£5.1million h ough he scheme [274]. These igu es a e a om he
300,000 social en e p ises and cha i ies ha could po en ially bene i
100 aming &al uism
om SITR, acco ding o Big Socie y Capi al [275]. Wha is causing such
a big di e ence? In a ecen call o e idence launched by he B i ish
Go e nmen , o ganisa ions ad oca ed o se e al changes sugges ing
ha such incen i es we e no i o pu pose [276]. In his ega d,
ou s udy con i ms ha ax incen i es a e no a game change o
people who a e no expe s in he ield. One may wonde whe he he
p oblem lies in he design o incen i e schemes o in he ac ha ax
incen i es hemsel es a e simply no a majo de e minan o in es o s’
decisions. O he coun ies ha e launched simila ax incen i e schemes
in he pas (i.e. F ance) and o he s (i.e., I aly) ha e jus ollowed. In
a ew yea s om now, i would be in e es ing o see he impac o
hese ecen ly implemen ed incen i es and un u he esea ch o
unde s and whe he iscal incen i es can s ill be conside ed as a main
d i e o in es o s’ beha iou o a e jus a nice add-on impac ing he
decision o ’only’ a ew.
The expe imen also b ough abou he linge ing scep icism abou
impac in es ing. Indeed, impac in es ing is s ill pe cei ed by some as
a suspicious hyb id whe e money-d i en ac o s, philan h opis s and
p ac i ione s (i.e., social en ep eneu s) a e cul u ally pola ised and
s ill s uggle o speak he same language [265]. By way o example,
one o he pa icipan s - and mo e speci ically a pa icipan om he
expe pool – epo ed eeling “almos ang y” a he buil -in ewa d
mechanism o he game. He con es ed no eeling included in he
scope o he expe imen , which acco ding o he pa icipan implici ly
assumed ha people can only be incen i ised by money; consequen ly,
in his iew, he expe imen was mean o p o i -o ien ed “ en u e
capi alis s” only. While he design o he game was me ely aimed a
esembling eal-li e ci cums ances, we did no p edic ha o e ing
a ewa d could ha e igge ed nega i e eac ions. In he same way,
ano he expe pa icipan ne e claimed he p ize, hus showing his
’pu e’ willingness o engage in he deba e and lack o esponsi eness
o mone a y incen i es.
5.2.3.1Conclusions
Impac in es ing aims o gene a e social and en i onmen al impac
alongside a inancial e u n. He e, we ha e un an expe imen wi h 602
pa icipan s o unde s and wha ’makes’ impac in es o s and wha
a e he d i e s o hei decisions. We apply logis ic eg ession analysis
on he acqui ed da a-se . One o he main weaknesses o he s udy
is he sample limi a ion o expe s. Howe e , we mus no e ha he
p ocess o inding expe s and ge hem o un he expe imen equi es
conside able esou ces. The e is no such a hing like a p e-de ined
a ailable da a-se o his, and he e o e ha ing access o expe s and
ensu ing hei pa icipa ion o he expe imen is a challenge in i sel ,
also due o hei ime limi a ion.

5.2 unde s anding d i e s when in es ing o impac 101
The main con ibu ion o his wo k is he domain insigh : ou
s udy shows ha pa icipan s a e gene ally a ou able o in es in
IIF, especially i hey a e women, olde people, o indi iduals who
we e al eady amilia wi h he impac in es ing ield (i.e., “expe s”).
Wi h e e ence o his las poin , while p io expe ience in he ield
has an impac on choices (
RQ1
), he e was no signi ican di e ence
be ween non-expe s who epo ed some o no p e ious knowledge
on impac in es ing. This migh lead o wo compe ing explana ions: i)
non-expe s who decla ed o ha e some knowledge on he ield knew
abou i only aguely; ii) simply knowing abou impac in es ing is
no enough, and p io expe ience a he han me e knowledge is a
mo e signi ican de e minan o choices.
Su p isingly, ex e nal incen i es such as ax b eaks do no appea
o be a game-change (
RQ4
), and u u e esea ch migh de e mine
when and why hey migh a ec in es o s’ decisions. On he o he
hand, when pa icipan s a e in o med o he isks a ached o hei
in es men , he likelihood o in es in an IIF dec eases (
RQ3
), bu i
inc eases when mo e in o ma ion abou he impac o hei in es men
is made a ailable (
RQ2
). Pa icula ly, we ha e seen ha isual aids
u he inc ease he in es o s’ willingness o choose an IIF ac oss all
ca ego ies analysed in his wo k. We no e ha addi ional e o s should
be made in aising awa eness abou impac in es men , especially by
policymake s and media ou le s. In e -sec o ial collabo a ion be ween
he public, p i a e and hi d sec o and academia (quad uple helix)
should be encou aged, as well as he in oduc ion o impac in es ing
in he cu iculum in inancial aining and educa ion.
Fu u e esea ches could bene i om a b oade da ase . Tax incen-
i es dese e special a en ion and esea che s could ocus on hose
coun ies ha ha e al eady designed and implemen ed policies on
his opic. An in e es ing wis o he esea ch could be in es iga ing
how beha iou changes i he choice o he pa icipan s is made public,
as an in e es in epu a ion-building and posi i e sel -b anding may
signi ican ly d i e people’s choices.
6
TRADING IN COMPLEX NETWORKS
Ma ke a Giso s,
Rue Cappe ille,
Camille Pissa o
Whoe e o e s o ano he a ba gain o any kind, p oposes o do his.
Gi e me ha which I wan , and you shall ha e his which you
wan , is he meaning o e e y such o e ; and i is in his manne
ha we ob ain om one ano he he a g ea e pa o hose good
o ices which we s and in need o .
Adam Smi h, The Weal h o Na ions
Up un il now, we ha e deal wi h scena ios whe ein he mani es-
a ion o humans’ p o-social endencies p o ides he mos e icien
ou comes o he g oup. Ne e heless, in some si ua ions, people o
companies coalescing can ha e ha m ul e ec s o social wel a e, such
as in he case o oligopolies and ca els. They a e de imen al by go-
ing agains one impo an ea u e o ma ke s: ee compe i ion. In an
ideal ma ke , he exis ence o many buye s and selle s would gua -
an ee long- un e iciency in a ba ie - ee en i onmen . As poin ed
by Adam Smi h, compe i ion would make ma ke p ices con e ge
o hei na u al le el and also push he economic sys em o highe
le els o p oduc i i y and inno a ions [29]. Thus, wi hou equi ing a
Le ia han [134], decen alized ade would wo k o he social wel a e
o he majo i y o people [277]. “buye s and selle s
a e in such ee
in e cou se wi h each
o he ha he p ices
o he same goods
end o equali y
easily and quickly.”
A. A. Cou no
[278]
Consequen ly, conce ning ma ke in e ac ions, compe i ion can be
seen as bene icial o he social good as coope a ion is in social dilem-
mas. None heless, in he eal wo ld, ac o s such as in o ma ion asym-
me ies and cumula i e ad an age can lead o ma ke ine iciency [279].
Speci ically, s uc u es cen alizing ma ke powe would unde mine
compe i ion, leading o monopolies and monopsonies de e mining
p ices [280]. The e o e, i is in he public in e es o iden i y such
s uc u es in o de o ensu e ee compe i ion endu es.
In his ega d, mos ma ke s show an unde lying ne wo k s uc u e
which has o be aken in o accoun i we a e o unde s and ma ke ou -
comes [55,281,282]. Indeed, economic in e ac ions a e in luenced by
geog aphic p oximi y and indi iduals’ ela ionships [283]. Mo eo e ,
global supply ne wo ks in ag icul u e, manu ac u ing, and se ices
a e a de ining ea u e o he mode n wo ld, and ading ou comes a e
a ec ed by all so s o middlemen connec ing p oduce s o buye s
[284]. Acco dingly, he e iciency and he dis ibu ion o su pluses
ac oss di e en pa s o hese ne wo ks depend on he decisions o
hei in e media ies. In pa icula , hei posi ion can make hem ex ac
a la ge ac ion o he ade su plus, and hey can be posi ioned in
such a way as o make ade ine icien [72].
103
104 ading in complex ne wo ks
Consequen ly, i is c ucial o iden i y he p inciples go e ning in e -
media ies beha iou , especially i hey decide simul aneously [279].
Fu he mo e, he e is a non- i ial in e play be ween decisions and
economic agen s’ links i he unde lying ne wo k exhibi s a complex
opology [62], such is common in eal sys ems [55,285]. Thus, o
imp o e ou insigh s abou hese ype o ma ke s, in his Chap e ,
we p esen esul s o p ice o ma ion expe imen s pe o med wi h
human subjec s loca ed in la ge complex ne wo ks. Mo eo e , he
obse ed beha iou leads us o c ea e an agen -based model yielding
mac oscopic pa e ns consis en wi h he expe imen al indings. In
sum, he esul s p esen ed in his Chap e show ha ne wo k opology
is a chie de e minan o p icing and e iciency.
6.1 e ec o ne wo k opology and node cen ali y on ading 111
No in Selec ed Pa h
In Selec ed Pa h
R26 SW26 R26 SW26
-2
0
2
Mean Change in P ice
SW26
R26
N Y N Y
0.00
0.25
0.50
P
A
B
Inc eased Dec eased
Figu e 6.4:Being o no in he cheapes pa h de e mines he in e medi-
a ies p ice inc eases. A:
Mean changes in he pos ed p ice condi-
ioned o ha e been ( igh ) o no (le ) in he selec ed cheapes
pa h in he p e ious ound o he andom ne wo ks o 26 nodes
(R26), and o he small-wo ld ne wo k o 26 nodes (SW26).
B:
P obabili y o inc ease (blue) and o dec ease (pink) he pos ed
p ice condi ioned o ha e been (Y) o no (N) in he selec ed
cheapes pa h, o each one o he s udied ne wo ks. The e o
ba s ep esen he 95
%
C.I. An ex ension o hese esul s including
he 50-nodes Random Ne wo k is displayed in Appendix Fig. b.2.
measu es, which explains why – in a si ua ion whe e p ices a e la gely
insensi i e o ne wo k loca ion – p o i s will be co ela ed wi h
sd∞( )
.
The obus ness o hese esul s agains he size and connec i i y o he
ne wo k is discussed in he Appendix Sec ion b.1.
So a , we ha e seen ha node cen ali y does no in luence ea nings
when we equally conside all he pa hs om S o D o compu e i , bu
i does when we conside only he sho es pa hs. This ac indica es
ha he weigh gi en o pa hs leng h is impo an o s udy he capaci y
o he nodes o ex ac su pluses. In o de o e i y his hypo hesis,
Fig. 6.3G shows he coe icien o de e mina ion
R2
o he eg ession
o in e media ies payo s on
sdα
as a unc ion o
α
. The bes i is
ob ained o
α∼12
, which indica es ha longe pa hs should ha e
signi ican ly smalle weigh han sho e ones. As he numbe o pa hs
g ows exponen ially wi h ne wo k size, SD-be weenness seems o be a
easible and good desc ip o o pa icipan s’ ea nings.
6.1.3Beha iou al ules
We ha e no ed ha pa icipan s’ beha iou is no de e mined by
ne wo k posi ion: c i icali y and classical measu es o cen ali y a e no
good p edic o s o he p ices pos ed by in e media ies. None heless,
esul s show di e ences in he p ices pos ed by ade s ac oss di e en
ne wo ks. E en i hese ne wo ks migh seem ela i ely small and

112 ading in complex ne wo ks
50
100
150
200
R26 SW26
Ne wo k
Cos
10
20
R26 SW26
Ne wo k
Mean P ice in Cheapes Pa h
Figu e 6.5:Nume ical esul s o he model execu ed o e he ne wo ks,
sou ce and des ina ion om he expe imen s.
Resul s shown
a e o 100 execu ions wi h 15 ounds o each ne wo k and
sou ce-des ina ion pai , excluding he i s ound. Ini ial p ices
a e boo s apped om he expe imen al alues. Values o
σ
and
ρ
a e ixed and co espond o mean alues o he expe imen ,
espec i ely, 2.60 and 1.2.
simila , hey a e no . The en i onmen (de ined as he se o all he
in o ma ion ha he indi iduals need o ac o in hei decisions) is
e y complex: he e a e many di e en pa hs passing h ough mos o
he ade s, hey need o ake in o accoun hei p ice as well as hose
o o he playe s, e c. I is hus easonable o assume ha he ade s
con on ing such a complex and dynamic en i onmen use ules o
humb, which on he o he hand, should no depend on he ne wo k.
In wha ollows, we de elop a model ha accoun s o indi idual
beha iou and o he di e ences obse ed expe imen ally.
Toge he wi h he ne wo k in o ma ion, he o he in o ma ion shown
o subjec s is whe he hey we e on he selec ed ading pa h. Fig. 6.4A
shows, o each one o he ne wo ks conside ed, he mean change
in p ice o he cases when he pa icipan was o was no along
he cheapes pa h in he p e ious ound. In he same way, Fig. 6.4B
shows he p obabili ies o inc ease and o dec ease he pos ed p ice
condi ioned o ha e been (Y) o no (N) in he cheapes pa h. Playe s
appea o ollow a simple ule, namely, o inc ease hei p ice i hey
we e on he cheapes pa h in he p e ious ound and o dec ease
i o he wise. Fu he mo e, he expec ed alues shown in Fig. 6.4A
poin ou ha success ul in e media ies keep inc easing hei p ices
and he e o e, wi hou su icien compe i ion, cos s and p ices would
always g ow.
We now build a simple agen based model (ABM) [305], as desc ibed
below:
i)
I node
u
belongs o a cheapes pa h a ime
, i will change i s
pos ed p ice on ime +1 by σ;
ii)
I node
u
does no belong o a cheapes pa h a ime , i will
change i s pos ed p ice on ime +1 by −ρ;
6.1 e ec o ne wo k opology and node cen ali y on ading 113
50
100
R SW R SW
0
50
100
Ne wo k
Cos
50
100
R SW R SW
0
5
10
15
20
25
Ne wo k
Mean P ice in Cheapes Pa h
Figu e 6.6:Nume ical esul s o he model o ne wo ks wi h 50 and 100
nodes.
Resul s shown a e o 100 execu ions wi h 15 ounds o
each ne wo k and sou ce-des ina ion pai , excluding he i s
ound. Ini ial p ices a e boo s apped om he expe imen al al-
ues. Values o
σ
and
ρ
a e ixed and co espond o mean alues
o he expe imen , espec i ely,
2.60
and
1.2
. Fo simila analyses
wi h andom ini ial p ices, see Appendix Fig. b.6.
iii) The minimum p ice a node can pos is 0.
ne wo k e iciency p ice p ice in CP cos leng h
R26 0.87 14.71 11.87 75.68 7.62
SW 26 0.66 15.14 12.56 94.32 8.97
Table 6.2:Nume ical esul s in expe imen al ne wo ks.
E iciency ( ac ion
o ounds in which he cheapes pa h cos was equal o o less
han he h eshold), and mean alues o he p ice, p ice in he
cheapes pa h, cos o he cheapes pa h, and cheapes pa h leng h.
Resul s ob ained om nume ical simula ions wi h each one o
he wo s udied ne wo ks wi h hei co esponding sou ce and
des ina ions.
To alida e his model we execu ed i by boo s apping he ini ial
p ices, he alue o changes i on he cheapes pa h (
σ
) and he alue
o changes i no (
ρ
). The esul s, shown in Fig. 6.5, indica e ha cos s
om simula ions ( esp. e iciency) a e highe ( esp. lowe ) in small-
wo ld ne wo ks han in andom ne wo ks ( (9659.3)=68.33,
p<0.001
),
in ag eemen wi h ou expe imen al esul s. Cos s eached ela i ely
high alues in some ounds, as he model does no inco po a e pa -
icipan s di ec esponse o he maximum cos h eshold. Table 6.2
also con i ms ha opological di e ences be ween he ne wo ks a e
d i ing he di e ences in cos .
Once we ha e shown ha he model cap u es e y well he expe i-
men al obse a ions, we e i y i he same phenomena a e obse ed
in la ge ne wo ks. Resul s o ne wo ks o size 50 and 100, shown
in Fig. 6.6and Table 6.3, a e also consis en wi h he expe imen al
114 ading in complex ne wo ks
da a, con i ming ha he ne wo k opology has a signi ican e ec on
ading ou comes: small-wo lds lead o highe cos s and lowe e i-
ciency. A simila analysis wi h andom ini ial p ices, hus unlinking
nume ical esul s om hose ob ained om he expe imen s, can be
ound in Appendix sec ion b.3.3and Fig. b.6. Resul s in Fig. b.6a e
compa ible wi h hose shown in Fig. 6.6, p o iding mo e e idence
abou he e ec s o he ne wo k s uc u e on p ices and cos s.
ne wo k e iciency p ice p ice in CP cos leng h
R50 0.98 13.12 7.03 44.76 7.68
SW 50 0.91 14.32 8.28 77.44 10.74
R100 0.97 12.65 5.53 46.50 10.05
SW 100 0.82 13.20 6.56 88.56 15.41
Table 6.3:Nume ical esul s o la ge ne wo ks.
E iciency ( ac ion o
ounds in which he cheapes pa h cos was equal o o less han
he h eshold), and mean alues o he p ice, p ice in he cheapes
pa h, cos o he cheapes pa h, and cheapes pa h leng h. Resul s
ob ained om nume ical simula ions wi h andom ne wo ks wi h
50 and 100 nodes (R 50, R 100) o he small-wo ld ne wo k wi h
50 and 100 nodes (R50, R 100).
6.1.4Topological p ope ies behind he di e ences in cos
Finally, we go one s ep u he in o de o explain wha lies behind he
di e ences ound in cos s. One possible heo e ical hypo hesis could
be ha cos s depend on compe i ion be ween pa hs. In ou se up, his
would be equi alen o assume ha cos s should dec ease wi h he
numbe o possible ways o each he des ina ion, i.e., he numbe
o independen (se s o ) pa hs om S o D. Speci ically, we expec
compe i ion o be p opo ional o he numbe
M
o node-disjoin pa hs
[306], as i cap u es he possible numbe o simul aneous independen
ades (see Appendix Sec ion b.3.1 o a deepe discussion on his
subjec ). Acco ding o his hypo hesis, he la ge he alue o
M
, he
lowe he cos . Ano he possible explana ion o he dependency o
cos s wi h he ne wo ks could be he s uc u al di e ences be ween
he la e . I is well known ha clus e ing coe icien s and a e age pa h
leng hs di e o he SW and he andom ne wo ks conside ed in ou
expe imen s (
p∈ {0.1,1}
[59]), and he e o e he obse ed di e ences
in cos could be ied o a ia ions in hose p ope ies.
In o de o e i y he p e ious hypo heses, we execu ed a e sion o
he model wi hou he maximum cos h eshold. Wi h his se up, we
can s udy long- e m e ec s a e a su icien ly la ge numbe o ounds
and unco e he cos endency. In his egime, we canno analyse
ne wo k e iciency, howe e , ne wo ks yielding highe cos should be
6.2 conclusions 115
mo e ine icien . No e ha he p oposed model allows ex apola ing
he obse ed beha iou o la ge ne wo ks wi h a la ge ange o alues
o
M
. Then, we can gene alize he obse ed expe imen al esul s o
la ge ne wo ks, which allow us o ind he ( heo e ically conjec u ed)
in luence o
M
on p ices. We an he algo i hm o
104
ounds and hen
we conside ed he inal cos o he ade o each con igu a ion. Resul s
o ne wo ks o size 26,50 and 1000 nodes a e shown in Figu es 6.7A,
6.7B, and 6.7C, espec i ely. Simula ions o ading dynamics on he
a o emen ioned ne wo ks indica e ha he numbe o node-disjoin
pa hs (
M
) be ween
S
and
D
is he bes indica o o inal cos . Fig.
6.7D shows ha as
M
g ows, he cos s a e educed so d as ically ha
hey go o 0 o
M>3
. Mo eo e , he nume ical esul s also e eal
ha o ne wo ks wi h he same alue o
M
, he cos g ows wi h he
a e age pa h leng h. Indeed, his dependency explains why cos s on
small-wo ld ne wo ks end o be la ge : hese ne wo ks ha e a la ge
a e age pa h-leng h. To show ha his inding is no a consequence
o di e ences in he leng h o he cheapes pa hs, Fig. b.4o he
Appendix displays, o he same simula ions, he cos s o he cheapes
pa h no malized by he numbe o nodes on i e sus he a e age
pa h leng h o he ne wo k. I can be seen ha he mean p ice o
nodes in he cheapes pa h also co ela es wi h he a e age pa h
leng h. In e es ingly, e en hough in his egime he di e ence in
he clus e ing is la ge han he di e ence in a e age pa h leng h,
he o me is no as good as an indica o o cos s (
R2=0.57
s
R2=0.79
, see Sec ion b.3.2, Table b.2, and Fig. b.5in he Appendix).
In summa y, hese esul s p o ide wo s ylized ac s ha may guide
u u e inqui ies in his line, namely, ading cos s will be null in se ups
wi h a ela i ely la ge numbe o node-disjoin pa hs and cos s should
be la ge in ne wo ks wi h la ge a e age pa h leng h.
6.2 conclusions
Ou expe imen al esul s indica e ha he ading ne wo k has a
powe ul e ec on bo h he p icing beha iou o in e media ies and
he o e all e iciency o he sys em, andom ne wo ks being mo e
e icien and showing signi ican ly lowe p ices han small-wo ld ne -
wo ks. Howe e , wi hin a ne wo k, p ices a e ela i ely insensi i e
o node loca ion, bu in e media ies wi h g ea e be weenness make
la ge p o i s. In o med by he expe imen al esul s, we in oduced
an ABM o p icing beha iou o unde s and ade s’ p icing. The key
inpu o he model is he expe imen al obse a ion ha in e medi-
a ies aise p ices when hey lie on he cheapes pa h and lowe hei
p ices o he wise. The model success ully ep oduced quali a i ely he
expe imen al esul s and allowed us o ex apola e and an icipa e ou -
comes o p icing and e iciency o scena ios in ol ing la ge ne wo ks
and longe imescales. Impo an enough, he model also enabled
116 ading in complex ne wo ks
R SW 123
A
0
3
6
9
0 2 4 6
A e age Pa h Leng h
Cos
B
0
5
10
15
20
25
0.0 2.5 5.0 7.5 10.0
A e age Pa h Leng h
Cos
C
0
5
10
15
0 5 10 15
A e age Pa h Leng h
Cos
D
0
2
4
6
8
12345
M
Cos
Figu e 6.7:Nume ical esul s o he model. A,B,C
: A e age inal cos (in
104
) o he cheapes pa h a e a pe iod o
104
ounds as a unc-
ion o he a e age pa h leng h o he ne wo k. Di e en panels
co espond o di e en ne wo k sizes: 26 (
A
), 50 (
B
), and 1000 (
C
)
nodes; colou s co espond o di e en ne wo k models: andom
(blue) and small-wo ld (magen a); and di e en shapes co e-
spond o di e en alues o he numbe
M
o disjoin pa hs. Fo
each con igu a ion, he e we e gene a ed 10000 ne wo ks o size
26,50, and 1000, acco ding o he Wa s-S oga z algo i hm [59]
wi h
p=0.1,1
and a e age deg ee om 2 o 10. The ini ial cos
was se o 0and he inc emen /dec emen a io was ixed o
he expe imen al alue (
σ/ρ=2.4
). Resul s o
M>5
a e no
shown as cos s con e ge as o 0.
D:
Mean alue o he cos o
he cheapes pa h e sus M o he same ne wo ks.

6.2 conclusions 117
he disco e y o wha a e he key de e minan s o cos , namely, he
numbe o node-disjoin pa hs om sou ce o des ina ion and he
ne wo k a e age pa h leng h. Ul ima ely, his explained he di e ences
in ou expe imen al esul s: in a small-wo ld ne wo k, he a e age
pa h leng h ends o be la ge and his leads o highe cos s and
lowe e iciency o ading in hese ne wo ks as compa ed o andom
ne wo ks.
O e all, ou wo k e eals ha he opology o ading ne wo ks is
key o de e mine hei e iciency and cos . I would be in e es ing o
u he es ou conclusions using eal da a on ading, in pa icula ,
he inding ha he a ailabili y o node-disjoin pa hs akes ading
cos s down. On he o he hand, ou insigh s may be use ul o he de-
sign o compe i ion-imp o ed ne wo ks o goods cu en ly o e p iced
due o in e media ion. Fu he esea ch on he ole o in o ma ion
p o ided o in e media ies and on o he ne wo k opologies will be
also ele an o add ess hese issues.
7
MODELLING THE EVOLUTION OF COOPERATION
In all hese scenes o animal li e which passed be o e my eyes, I saw
Mu ual Aid and Mu ual Suppo ca ied on o an ex en which
made me suspec in i a ea u e o he g ea es impo ance o he
main enance o li e, he p ese a ion o each species, and i s u he
e olu ion.
Mu ual Aid: A Fac o o E olu ion, K opo kin
Figu e wi h
D awe s o a
Fou -pa Sc een,
Sal ado Dali
The esul s p esen ed in he las chap e s ha e shown how expe i-
men s can be used o ob ain knowledge o human beha iou . A nex
s ep in he scien i ic dynamics is o mula ing new heo ies ha can be
es ed by new expe imen s [30], o looking a he implica ions ha he
obse ed beha iou can ha e in sys ems ha canno be ep oduced in
he labo a o y, such as we ha e done in Sec ion 6.1.3. This especially
impo an when s udying social sys ems, gi en ha humans usually
li e in la ge g oups [2,3], a condi ion ha is un easible o being e-
p oduced in a con olled expe imen . E en hough la ge sys ems can
be eplica ed o some ex en [17], some scena ios a e jus impossible,
such as ep oducing he e olu iona y p ocess o humans o o he
animals. In hese si ua ions, compu e simula ions a e p obably e-
sea che s’ bes ool [307], cap u ing eme gen phenomena in si ua ions
ha closed- o m solu ions canno be ob ained [115,308]. “This is he essence
o in ui i e
heu is ics: when
aced wi h a di icul
ques ion, we o en
answe an easie one
ins ead, usually
wi hou no icing he
subs i u ion.”
Daniel Kahneman,
[309]
Agen -based models (ABM) a e especially impo an in his ega d,
[305], belonging o a hi d way o doing science acco ding o Robe
Axel od, ha ing s ong assump ions as deduc ion, bu coming o con-
clusions o he simula ed da a ia induc ion [307]. Simula ions o ABM
allow explo ing answe s o complex ques ions, such as one unde lying
his hesis: how he coope a i e beha iou obse ed in humans ha e
o igina ed? This ques ion is no ee om con o e sies, as we discuss
in Sec ions 2.4.4and 8.1. We a emp o con ibu e o his discussion
in his Chap e by using e olu iona y game heo y, bu wi hou he
ha d assump ions o pu e s a egies. Ins ead, we ely on heu is ics,
which co espond o he me hod used by humans when making deci-
sions [192]. Mo eo e , we use e olu iona y algo i hms [310] o model
he dynamics o s a egies selec ion and, hus, unco e he eme ging
heu is ics. As we p esen in he nex sec ion, ou indings esul ed
o be e y insigh ul, shedding some ligh in how he e olu iona y
p ocess migh di e be ween humans and o he non-human animals.
119
120 modelling he e olu ion o coope a ion
7.1
dynamics o heu is ics selec ion o coope a i e
beha iou
Dynamics o heu is ics selec ion o coope a i e beha iou ,
unde e iew.
F. Maciel Ca doso, C. G acia-Láza o, & Y. Mo eno
Game heo y cons i u es a powe ul amewo k o he ma hema i-
cal s udy o social dilemmas [19,20]. Wi hin his amewo k, he mos
ep esen a i e and widely used game o model coope a ion, he P is-
one ’s Dilemma, has become a pa adigm o modelling he e olu ion
o coope a i e beha iou [23]. The P isone ’s Dilemma mimics he
wo s possible scena io o coope a ion in which sel ishness always
p o ides a highe indi idual bene i han coope a i e beha iou . Ini ial
p edic ions indica ed he social op imum would no be eachable by
a ional sel ish indi iduals i he emp a ion o de ec ing (
T
) exceeded
he ewa d o coope a ing
R
. None heless, coope a ion is pe asi e
in human and animal socie ies [311–313], and a as li e a u e has
demons a ed how coope a ion can h i e in he p esence o an ap-
p op ia e e olu iona y p ocess [24,26,91,111,113,115,314–316]. The
possible si ua ions whe e coope a ion migh lou ish a e endless, and
we a e jus beginning o unco e he ing edien s behind he complexi y
obse ed in eal sys ems [40,155]. Consequen ly, heo e ical s udies
usually ocus on simpli ica ions, such as indi iduals beha ing acco d-
ing o ixed pu e s a egies [111,115] o some a bi a y se o hem
[317,318]. Ye , he easoning and mo i a ions o humans a e mo e
sophis ica ed and complex han pu e s a egies and decisions a e usu-
ally aken ac o ing in many ing edien s, weigh ing hem di e en ly
[192]. In o he wo ds, gene ally speaking, he selec ion o s a egies
akes place in complex sys ems whe ein imp ecise beha iou and he
en i onmen a e inpu s o each o he in a pe pe ual eedback loop
[319].
In his line, beha iou al economics has shown ha humans espond
in unexpec ed ways [33,193] and o en seem o possess ha dwi ed
heu is ics while ac ing in expe imen al si ua ions [320,321]. Expe i-
men s ha e also shown ha humans au oma ic esponses a e modelled
by expe iences om daily-li e, building heu is ics o in ui ions which
end o a ou coope a ion [150,154]. The e o e, i is plausible ha
coope a i e socie ies a e sus ained by exis en heu is ics, main ained
by no ms [2,101] o biological ac o s [82,155,320], ha ha e esul ed
om a selec ion dynamics. I is hus impe a i e o unde s and how
such possible heu is ics ha e e ol ed, which will allow explaining
he ing ained mechanisms behind he beha iou obse ed in li ing
beings.
He e, we in es iga e he e olu ion o coope a i e s a egies h ough
an agen -based model o heu is ics selec ion inspi ed by e olu iona y
7.1 dynamics o heu is ics selec ion o coope a i e beha iou 127
0 0.0001 0.05 1
LTT
RRN
0 0.25 0.5 0 0.25 0.5 0 0.25 0.5 0 0.25 0.5
0.00
0.25
0.50
0.75
1.00
0.00
0.25
0.50
0.75
1.00
0.00 0.25 0.50 0.75 1.00
F ac ion o coope a i e ac ions
Gene a ion
(105)
Figu e 7.3:F ac ion o coope a i e ac ions a he end o each gene a ion
.
Columns co espond o di e en mu a ion alues (0,0.0001,0.05,
1) and ho izon al panels o di e en ne wo ks (LTT, RRN). Agen s
ha e memo y
m=1
and 100 ealiza ions a e pe o med o each
mu a ion alue and ne wo k. The colou s o he lines co espond
o he a e age o he las 1000 gene a ions.
gies o p e ail and de ec ion ends o inc ease, howe e , a su icien ly
small mu a ion p obabili y will gua an ee ha he sys em e ol es o a
coope a i e equilib ium.
7.1.2.1O he payo alues
To ensu e ha ou esul s a e obus wi h espec o di e ences in
he payo alues, we an simula ions o di e en alues o he
emp a ion pa ame e
T
. To make ou esul s compa able o p e-
ious wo k, we used he one-dimensional pa ame iza ion o pay-
o s used by Nowak e . al [111]. In his e sion,
R=1
,
P=e
,
S=0
, and
T
a ies om 1 o 2, wi h
e
being a alue close o ze o.
As we conside no malized e sions, he payo he e is de ined by
T=T0/hki;R=1/ hki;P=0.01/ hki;S=0
, wi h
T0
a ying om 1
o 2. Resul s o memo y 0and 1a e shown in Fig. 7.4. The esul s
show ha wi hou memo y, coope a ion is only a ainable when
T0=1
and low mu a ion. Howe e , when agen s ha e memo y o hei las
in e ac ion, coope a ion endu es e en when he emp a ion o de ec
is a ound 2.
7.1.2.2Heu is ics and S a egies
In his sec ion, we ocus on he composi ion o he popula ions in he
di e en egimes. I is no s aigh o wa d o e alua e how genes and

128 modelling he e olu ion o coope a ion
0
1
1.00
1.25
1.50
1.75
2.00
pm
T'
0.00
0.25
0.50
0.75
1.00
A e age
Coope a ion
0.00 0.25 0.50 0.75 1.00 0.00 0.25 0.50 0.75 1.00
Figu e 7.4:A e age coope a ion a he s a iona y s a e
. The le panel shows
esul s o
m=0
and he igh panel o
m=1
.100 simula ions
we e done o each
pm
and
T0
combina ion. Colou coding co e-
sponds o he a e age o e all ealiza ions and a ies om blue
(1) o yellow (0).
a iables in e ac , hence, i is ha d o de e mine i agen s a e going
o coope a e o no in a speci ic si ua ion. A i s s ep is o in es i-
ga e wha a e he gene alues in coope a i e and non-coope a i e
equilib ia. Fig. 7.5show he dis ibu ions o genes o wo mu a ion
alues:
pmu =0.05
and
pmu =1
, whe ein e olu ion leads o mos ly
coope a ion and o mos ly de ec ion, espec i ely. Simula ions in bo h
LTT and RRN ne wo ks yielded simila dis ibu ions, indica ing he
p esence o a common e olu iona y pa e n.
When he majo i y o he popula ion coope a es (
pmu =0.05
),
β0
,
C1
, and
R1
ha e a clea igh -modali y wi h mos o hese alues being
highe han 0. Con e sely,
D1
is le -modal wi h a clea peak a ex-
eme nega i e alues, while
P1
shows a so e end owa ds nega i e
alues. This implies ha when coope a ion h i es, agen s ha e a base-
line coope a i e esponse and end o ecip oca e coope a ion bo h
di ec ly and indi ec ly. On he o he hand, he agen s punish de ec o s
igo ously and ha e a mild nega i e esponse o o he agen s’ payo ,
p obably as a means o punish de ec o s, as only de ec o s can a ain
he highes payo s. In e es ingly, he dis ibu ions o
β0
indica e ha
he eme ging s a egies a e willing o coope a e e en in a one-sho
game wi h an unknown playe as show in Fig. 7.7, albei his is no
he expec ed beha iou o
m=0
. In he o he ex eme, o
pmu =1
,
de ec ion p e ails, and genes alues indica e he unde pinnings o
his end. All dis ibu ions a e igh -skewed, wi h
β0
and
D1
ha ing
a no iceable peak a he lowes possible alues. Thus, when mu a ions
a e oo equen agen s a e much mo e likely o exploi and punish,
leading de ec ion o be he de aul s a egy. Too much d i will make
i impossible o coope a i e heu is ics o be selec ed, and hey will
anish in he popula ion.
7.1 dynamics o heu is ics selec ion o coope a i e beha iou 129
Figu e 7.5:Dis ibu ion o genes’ exp essed alues.
Densi ies o genes al-
ues o simula ions on LTT and RRN g aphs o
m=1
. Top
panels show dis ibu ions o
pmu =0.05
and bo om panels
o
pmu =1
. The e ical dashed line indica es sepa a e egions
whe ein he ma ginal p obabili y o coope a e would be smalle
(nega i e gene alues) and g ea e (posi i e gene alue) han 0.5.
These las esul s p o ide a pic u e o he geno ype space. Howe e ,
he e is s ill he need o iden i y which s a egies ha e eme ged. When
s udying e olu iona y games, i is always challenging o b idge he
gap be ween he geno ype and pheno ype spaces [323]. In ou model,
he p o ile o agen s’ ac ions would co espond o obse able pheno-
ypes, ye i is no s aigh o wa d o speci y a me hod o heu is ics
classi ica ion. An unsupe ised p ocedu e would all in o he p oblem
o how o iden i y he g oups encoun e ed, i.e., how o de e mine o
which known s a egies hey co espond. The e o e, he e we adop ed
an app oach ha consis ed o classi ying agen s by looking a wha
would be hei esponses o he mos basic s a egies: a pu e de ec o
and a pu e coope a o . Namely, we looked a whe he agen s we e
likely o coope a e o de ec wi h agen s ha ing a his o y co espond-
ing o each o he wo pu e s a egies. Fo ins ance, a ull de ec o
would always ha e de ec ed wi h
u
(
C1
,u=0
,
D1
,u=1
), wi h i s
o he neighbou s (
R1
,u=0
), and would ha e an expec ed payo (
π1
)
co esponding o hese ac ions.
Table 7.2illus a es he a iables con ained in he memo y o agen
u
wi h espec o a playe
, co esponding o he wo pu e s a egies
o
m=1
. All he alues a e gi en s aigh o wa dly, expec o
π1
.
Payo s alues a e mo e complica ed, as hey depend on he playe s
wi h whom hey a e playing wi h, which we canno de ine a p io i. We
130 modelling he e olu ion o coope a ion
Pu e Coope a o Pu e De ec o
C1
,u1 0
R1
,u1 0
π1
hπCi hπDi
D1
,u0 1
Table 7.2:Pu e s a egies memo y.
Pas his o y o he wo basic s a egies
acco ding o wha would ha e been played by hem o m=1.
Pu e Coope a o Pu e De ec o
FC C C
FD D D
CC C D
GCC C-
CD - D
Bully D C
Random - -
Table 7.3:Classi ica ion o heu is ics acco ding o hei esponses o he
wo pu e s a egies:
pu e de ec o and pu e coope a o . We con-
side ha agen s coope a e (
C
) o de ec (
D
) i hei p obabili y o
coope a e is g ea e han (1−σ)o smalle han σ, espec i ely.
decided o use he a e age payo o indi iduals which coope a ed and
de ec ed wi h all hei neighbou s o he pu e coope a o and pu e
de ec o , espec i ely. The e o e,
hπCi=hπ
ii∀i∈R1,∀ ∈[1,100]
and
hπDi=hπ
ii∀i∈R0,∀ ∈[1,100]
, whe ein
R1
( esp.
R0
) co esponds
o he se o agen s which coope a ed wi h all ( esp. none) o hei
neighbou s in he las ime s ep.
We hen, use he h eshold
σ
o di ide he plane
(ρC,ρD)
. Namely,
we designa e as coope a ion when
ρ>(1−σ)
, de ec ion as
ρ<σ
, and
andom (-) when
σ≤ρ≤(1−σ)
. This p ocess esul s in he p oposed
classi ica ion is shown in Table 7.3. We conside ed s a egies analo-
gous o known ones, namely: Full Coope a o (FC), coope a es wi h
bo h pu e coope a o s and pu e de ec o s; Full De ec o (FC), de ec s
wi h bo h; Condi ional Coope a o (CC), ecip oca es coope a ion and
de ec s o he wise; Gene ous Condi ional Coope a o (GCC), ecip oca es
coope a ion and can coope a e andomly wi h de ec o s; Condi ional
De ec o (CD), coope a es andomly wi h coope a o s and always de-
ec s wi h de ec o s; Bully, de ec s wi h coope a o s, bu coope a es
wi h de ec o s; Random, beha e andomly wi h bo h pu e s a egies.
We labelled agen s ha could no be classi ied by his p ocess as
Unde ined.
7.1 dynamics o heu is ics selec ion o coope a i e beha iou 131
In Fig. 7.6, we show he equencies o each s a egy om sim-
ula ions o he heu is ics selec ion dynamics. Top panels (
A
) show
s a egies o a la ice and bo om panels (
B
) o RRN ne wo ks. Resul s
in bo h ne wo ks ypes a e e y consis en : when he mu a ion is low
(
pmu =0.05
), mos o he agen s end o be coope a o s o condi ional
coope a o s (mean ac ion is 0.9wi h a s anda d de ia ion o 0.07):
CC cons i u es mos o he s a egies, ollowed by a small ac ion o
GCC and FC playe s. In con as , when mu a ion is high (
pmu =1
),
FD and CD cons i u e he majo i y (mean=0.66, sd=0.038) o agen s.
Howe e , a mino i y o CC playe s can pe sis (mean=0.17, sd=0.022),
which explains he exis ence o a small ac ion o coope a i e ac ions
e en in his egime.
7.1.2.3Explo ing kin disc imina ion: a i s ex ension.
I is known ha coope a i e beha iou can eme ge and be sus ained
by ac o s ha do no depend on playe s his o y o decisions. Namely,
gene ic ela edness o kinship plays a key ole in he e olu ion o
coope a ion in na u e [79,82,83,89]. Kin selec ion is pe asi e [311,
312], despi e con o e sies o e i s ole in pa icula phenomena [84,
107,108,110,330,331]. Indeed, hese disag eemen s indica e he need
o in es iga e he ole played by gene ic ela edness in each speci ic
scena io [84]. The e o e, o add ess his ques ion, we ake such mecha-
nisms in o accoun in he e olu iona y dynamics o heu is ics selec ion.
Namely, we ha e ex ended he p e ious analysis and conside ed ha
agen s could e alua e an addi ional a iable ha accoun s whom hey
a e in e ac ing wi h, speci ically, gene ic p oximi y, which is one main
mechanism ensu ing in e ac ions occu among ela ed indi iduals
[79].
We added o he agen s’ ch omosome a gene
K
o accoun o gene ic
ela edness wi h he in e ac ing agen . Ope a ionally, we conside
ha his kinship ela ion is gi en by he Jacca d index o pai s o
agen s’ ch omosomes. No e ha we a e no speci ying a me hod o
kin selec ion, bu allowing he heu is ics o ake in o conside a ion
agen s simila i y when deciding o coope a e o no . Enabling, hus,
an es ima ion o he ele ance o gene ic ela edness by e alua ing he
weigh o ganically gi en o he heu is ics’ new gene.
Resul s o simula ions on a la ice a e p esen ed in Figu e 7.8. Figu e
7.8A shows he ac ion o coope a ion a he s eady-s a e bo h o
ou p e ious model (Non-Kin) and o he ex ended model (Kin). The
e olu ion leads o simila scena ios in bo h cases, indica ing ha he
p esence o he (
K
) gene did no enhance no unde mine coope a ion
signi ican ly, hough he e is one modes excep ion. Fo heu is ics
wi hou memo y (
m=0
) and low mu a ion, he e is a modes inc ease
in he le el o coope a ion. A a iance wi h he model in a la ice,
when he e is no mu a ion, he ac ion o coope a i e ac ions can be
di e en om ze o in an RRN ne wo k, as shown in Fig. 7.9A. This
132 modelling he e olu ion o coope a ion
A
B
Figu e 7.6:Eme ging S a egies.
F equency o each s a egy in execu ions
in LTT ( op panels
A
) and RRN (bo om panel
B
) ne wo ks o
pmu =0.05
,
σ=0.3
and
m=1
. Each ed do co espond o
he ac ion o he s a egy in a simula ion and he his og am
o ac ions o each s a egy is shown e ically, wi h da kes
colou s ep esen ing a highe numbe o occu ences.

7.2 conclusions 133
LTT
RRN
0.05
1
0.00 0.25 0.50 0.75 1.00 0.00 0.25 0.50 0.75 1.00
0
10000
20000
30000
40000
0
10000
20000
30000
40000
ρonesho
coun
Figu e 7.7:Coope a ion p obabili y in one-sho games
. Dis ibu ions a e
calcula ed o e agen s o he inal gene a ion o
m=1
in a
la ice (le panel) and in andom egula ne wo ks ( igh panel).
P obabili y is calcula ed conside ing ha agen s do no ha e
access o o he pa icipan s in o ma ion, hus, only
β0
is used in
he sigmoid. Top panels show dis ibu ions o
pmu =0.05
and
bo om panels o pmu =1.
demons a es how impo an he kin iden i ica ion mechanism can be
in an adequa e en i onmen .
Despi e he negligible di e ences in ou comes, he e is a subs an ial
e ec on agen s’ ch omosomes. Fig. 7.8B ( esp. 7.9B) shows ha includ-
ing he possibili y o weigh gene simila i y changes he alues o all
o he genes signi ican ly in la ices ( esp. RRN ne wo ks). Fo
m=1
,
coope a ion is s ongly de e mined by he (
K
) gene, and genes o
di ec ecip oci y and cons an esponse becomes nega i e o neu al.
The la e implies ha mos agen s will no coope a e in one-sho
in e ac ions wi h un ela ed indi iduals, as shown in Fig. 7.10, demon-
s a ing a signi ican di e ence om he agen s wi hou he
K
gene.
The e s ill is a mos ly posi i e esponse o indi ec ecip oci y and a
nega i e o punishmen , while he weigh gi en o pa icipan s payo
in e s. This esul poin s o a compelling message: when heu is ics
can e alua e gene ic ela edness, he ones ha do ha will ha e a
highe ep oduc ion, he e o e esul ing in mo e adap ed heu is ics.
None heless, in o ma ion om pas in e ac ions is s ill equi ed, wi h
punishmen and ecip oci y playing a ole.
7.2 conclusions
Na u al selec ion has shaped he e olu ion o all so o li e o ms. Ad-
an ageous s a egies endu e while o he s dwindle in a ne e -ending
p ocess o adap a ion. Fundamen al ques ions ega ding he eme -
gence o coope a i e beha iou in social dilemmas ha e o be s udied
134 modelling he e olu ion o coope a ion
Figu e 7.8:E olu ion o heu is ics wi h kin iden i ica ion on LTT. A
F ac-
ion o coope a i e ac ions a he s eady s a e as a unc ion o
he mu a ion p obabili y. Colou s and shapes co espond o di -
e en memo y (
m
) alues. A e ages plus .95 con idence in e al
o 100 ealiza ions a e p esen ed o each mu a ion (
pmu
) alue.
B
Densi ies o genes alues o simula ions on LTT g aphs o
pmu =0.05
and
m=1
. The e ical dashed lines sepa a e he
egions whe ein he p obabili y o coope a e would be smalle
(gene alue smalle han 0) and g ea e (gene alue smalle han
0) han 0.5.
7.2 conclusions 135
Figu e 7.9:E olu ion o heu is ics wi h kin iden i ica ion on RRN. A
F ac-
ion o coope a i e ac ions a he s eady s a e as a unc ion o
he mu a ion p obabili y. Colou s and shapes co espond o di -
e en memo y (
m
) alues. A e ages plus .95 con idence in e al
o 100 ealiza ions a e p esen ed o each mu a ion (
pmu
) alue.
B
Densi ies o genes alues o simula ions on RRN g aphs o
pmu =0.05
and
m=1
. The e ical dashed lines sepa a e he
egions whe ein he p obabili y o coope a e would be smalle
(gene alue smalle han 0) and g ea e (gene alue smalle han
0) han 0.5.
136 modelling he e olu ion o coope a ion
LTT
RRN
0.05
1
0.00 0.25 0.50 0.75 1.00 0.00 0.25 0.50 0.75 1.00
0e+00
2e+05
4e+05
6e+05
0e+00
2e+05
4e+05
6e+05
ρonesho
coun
Figu e 7.10:Coope a ion p obabili y in one-sho games o he model
wi h he kin iden i ica ion gene
. Dis ibu ions a e calcula ed
o e agen s o he inal gene a ion o
m=1
in a la ice (le
panel) and in andom egula ne wo ks ( igh panel). P obabili y
is calcula ed conside ing ha agen s do no ha e access o o he
pa icipan s in o ma ion, hus, only
β0
is used in he sigmoid.
Top panels show dis ibu ions o
pmu =0.05
and bo om panels
o pmu =1.
in he ligh o e olu iona y mechanisms. Undoub edly, eme ging be-
ha iou is in insically dependan on he indi iduals unde s udy, e.g.,
humans commonly coope a e in la ge socie ies composed o un ela ed
indi iduals, while g oups o animals a e ha dly g ea e han a ew
hund ed [3]. In pa icula , a iance in humans is especially ele an ,
as beha iou is deeply a ec ed by he speci ics o he in e ac ions
and he cul u e o he indi iduals [15,40]. Mo eo e , gi en ha i is
an eme gen phenomenon, beha iou can be deeply a ec ed by he
complex opology o in e ac ions [117]. In an a emp o p o ide a
amewo k o such scena ios, he e we explo e a model ha allows
un a elling wha could be he d i e s o coope a ion by a heu is ics
selec ion p ocess.
By explo ing heu is ics ha make use o agen s beha iou al in o -
ma ion o s ochas ically de e mine hei decisions in i e a ed p isone s’
dilemma games ac oss gene a ions, we ha e shown ha , in a easible
en i onmen , e olu ion will d i e heu is ics owa ds coope a ion e en
when de ec ion is expec ed o pu e s a egies. In hese scena ios,
ecip oci y and punishmen a e he main ing edien s o coope a o s’
decision-making, and mos s a egies will ollow condi ional coope a-
ion. The ac ion o coope a i e decisions dec eases wi h an inc ease
in he mu a ion a e, none heless, o small mu a ion a es he sys em
eaches a coope a i e equilib ium. Wi hou mu a ion, he con igu a-
ion o he ini ial s a e is c i ical and he sys em can ge apped in
equilib ia o meag e coope a ion. Inc easing he memo y o indi idu-