Sasaki, Ta suya; Yamamo o, Hi oshi; Okada, Isamu; Uchida, Sa oshi
A icle
The e olu ion o epu a ion-based coope a ion in egula
ne wo ks
Games
P o ided in Coope a ion wi h:
MDPI – Mul idisciplina y Digi al Publishing Ins i u e, Basel
Sugges ed Ci a ion: Sasaki, Ta suya; Yamamo o, Hi oshi; Okada, Isamu; Uchida, Sa oshi (2017) : The
e olu ion o epu a ion-based coope a ion in egula ne wo ks, Games, ISSN 2073-4336, MDPI,
Basel, Vol. 8, Iss. 1, pp. 1-16,
h ps://doi.o g/10.3390/g8010008
This Ve sion is a ailable a :
h ps://hdl.handle.ne /10419/168007
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games
A icle
The E olu ion o Repu a ion-Based Coope a ion in
Regula Ne wo ks
Ta suya Sasaki 1,*, Hi oshi Yamamo o 2, Isamu Okada 3and Sa oshi Uchida 4
1Facul y o Ma hema ics, Uni e si y o Vienna, 1090 Vienna, Aus ia
2Facul y o Business Adminis a ion, Rissho Uni e si y, 141-8602 Tokyo, Japan; [email p o ec ed]
3Facul y o Business Adminis a ion, Soka Uni e si y, 192-8577 Tokyo, Japan; [email p o ec ed]
4Resea ch Cen e o E hicul u e S udies, RINRI Ins i u e, 102-8561 Tokyo, Japan; [email p o ec ed].jp
*Co espondence: [email p o ec ed]; Tel.: +43-1-4277-50774
Academic Edi o : A ila Szolnoki
Recei ed: 14 Sep embe 2016; Accep ed: 13 Janua y 2017; Published: 21 Janua y 2017
Abs ac :
Despi e ecen ad ances in epu a ion echnologies, i is no clea how epu a ion
sys ems can a ec human coope a ion in social ne wo ks. Al hough i is known ha wo o
he majo mechanisms in he e olu ion o coope a ion a e spa ial selec ion and epu a ion-based
ecip oci y, heo e ical s udy o he in e play be ween bo h mechanisms emains almos uncha ed.
He e, we p esen a new indi idual-based model o he e olu ion o ecip ocal coope a ion
be ween epu a ion and ne wo ks. We compa a i ely analyze ou o he leading mo al assessmen
ules—shunning, image sco ing, s e n judging, and simple s anding—and base he model on he
gi ing game in egula ne wo ks o Coope a o s, De ec o s, and Disc imina o s. Disc imina o s
ely on a p ope mo al assessmen ule. By using indi idual-based models, we show ha he ou
assessmen ules a e di e en ly cha ac e ized in e ms o how coope a ion e ol es, depending on he
bene i - o-cos a io, he ne wo k-node deg ee, and he obse a ion and e o condi ions. Ou indings
show ha he mos ole an ule—simple s anding—is he mos obus among he ou assessmen
ules in p omo ing coope a ion in egula ne wo ks.
Keywo ds:
e olu ion o coope a ion; indi ec ecip oci y; s uc u ed popula ion; social no m;
p i a e in o ma ion
PACS Classi ica ion: 87.23.-n; 02.50.Ey
JEL Classi ica ion: C72; C73; D63; D64; D82; D85
1. In oduc ion
Repu a ion is one o he mos p ac ical ools o measu ing pa ne s’ quali y and incen i izing
pa ne s’ beha io s [
1
]. Repu a ion is hus o en compa ed o cu ency [
2
]. The concep o a epu a ion
sys em has been applied o a ious si ua ions, e.g., om gossip among neighbo s o a a ing and
e iew o e-Bay (San Jose, CA, USA), Ube (San F ancisco, CA, USA), T ipAd iso (Needham, MA,
USA), e c. Game- heo e ical s udies ha e shown ha epu a ion can acili a e he e olu ion o ecip ocal
coope a ion in he con ex o indi ec ecip oci y [
3
–
6
]. Indi ec ecip oci y h ough epu a ion wo ks
in a pee - o-pee ashion by conside ing condi ional coope a ion: o help his/he co-playe who has
a good epu a ion ye also e use o help he co-playe who has a bad epu a ion [
7
]. The c ucial aspec
o epu a ion-based indi ec ecip oci y is how indi idual p o iles a e assessed in e ms o hei image
sco e o mo ally judged as being good o bad [
8
,
9
]. The mapping o indi idual p o iles o he image
sco e is called he mo al assessmen ule [
10
]. Bo h classi ica ion and analysis o he mo al assessmen
Games 2017,8, 8; doi:10.3390/g8010008 www.mdpi.com/jou nal/games
Games 2017,8, 8 2 o 16
ule in he si ua ion o social exchange ha e a ac ed b oad a en ion in he ields o e olu iona y
biology and he social sciences [7].
In his s udy, we shed ligh on he e ec s o popula ion s uc u es on he e olu ion o
epu a ion-based indi ec ecip oci y. Spa ial selec ion is ano he majo ac o o he e olu ion
o coope a ion [
11
–
14
]. The e is a as amoun o game- heo e ical li e a u e on he e olu ion
o coope a ion h ough di ec ecip oci y [
15
–
24
] o ups eam ecip oci y [
25
–
27
] in s uc u ed
popula ions. He e, we conside ne wo ks o esiden s in which he epu a ions o neighbo s a e
key pieces o in o ma ion used o de e mine no only he mo e bu also he pa ne in he nex
in e ac ion. This allows us o explo e an indi ec in e ac ion, which can be desc ibed as ollows:
“I know you did no help a good esiden in he pas (and hus you look bad); he e o e, oday I will
no help you”. Al hough his si ua ion is qui e popula in eal-li e se ings, i has had li le explo a ion
in game- heo e ic models. In his pape , we conside ha he ocal playe ’s ac ion is de e mined no
only by how he neighbo beha ed o he ocal playe bu how he neighbo beha ed o he neighbo ’s
neighbo . Simila ly, he neighbo ’s las ac ion o he neighbo ’s neighbo may be de e mined by how
he neighbo ’s neighbo p e iously beha ed o he neighbo ’s neighbo ’s neighbo . Thus, epu a ion is
good a bo h accumula ing and abs ac ing his in o ma ion, and popula ion s uc u es may a ec no
only he shape o indi idual in e ac ion wi hin a neighbo hood bu also he o ma ion o indi idual
epu a ional in o ma ion.
Posi i e e ec s o he in e play o popula ion s uc u es and epu a ion-based condi ional
beha io s as such ha e been nume ically in es iga ed since app oxima ely 2000 [
28
–
30
]. Models in
p e ious s udies mos ly combined punishmen , pa ne choice, o ne wo k ewi ing [
31
–
37
]. No ably,
punishmen , pa ne choice, and ne wo k ewi ing a e o en cos ly [38,39].
In his s udy, we would like o b eak in o an unexplo ed a ea o he mo al assessmen ules. To da e,
he assessmen ules explo ed o spa ial indi ec ecip oci y ha e included only he simples — he
image-sco ing ule [
40
]. Image sco ing depends only on he ocal playe ’s las ac ion, which hus is
called he i s -o de assessmen ule [
10
]. Recen expe imen al e idence has shown ha a ce ain
ac ion o people is likely o use no only he in o ma ion o he ocal indi idual bu also he opponen ’s
p o ile [
41
]. Assessmen ules ha conside he opponen ’s epu a ion as well as he ocal playe ’s
las ac ion a e called second-o de assessmen ules [
10
]. Second-o de assessmen ules may equi e
mo e cogni i e loads and ha e highe in o ma ion cos s han image sco ing [
42
,
43
]; hus, hey may
be mo e likely o in i e hose who eeload on o he s’ e o s in assessmen [
44
]. Howe e , ecen
ad ances in in o ma ion and communica ion echnology (ICT) a e lowe ing he h eshold o applying
such complica ed assessmen ules in indi ec ecip oci y. An ins i u ional p e-assessmen sys em can
also help de e he assessmen eeloade [45].
The majo second-o de assessmen ules consis o simple s anding [
3
,
46
,
47
], s e n judging [
48
,
49
],
and shunning [
50
] (Table 1). Howe e , li le is known abou how hese second-o de ules a ec he
e olu ion o coope a ion by spa ial indi ec ecip oci y [
51
]. The e o e, he p ima y aim o his pape is
o compa a i ely analyze he ou ep esen a i e assessmen ules o simple s anding, s e n judging,
shunning, and image sco ing in e olu iona y games on social ne wo ks. We base e olu iona y gi ing
games on egula ne wo ks and conside public and p i a e in o ma ion wi h assessmen e o s.
As we will show in he ollowing chap e s, ou model can lead o clea ly dis inguishing among he
ou ep esen a i e assessmen ules. Ou esul s e eal ha simple s anding, which is he mos
ole an among he ou ules, is he mos obus in sus aining ull coope a ion; in he o he h ee
ules, coope a ion becomes less equen and commonly does so as he node deg ee inc eases and he
assessmen e o becomes p i a e.
In he ollowing sec ions, we p opose an agen -based model o s udying spa ial indi ec
ecip oci y (Sec ion 2), nume ically analyze he e olu ion o spa ial indi ec ecip oci y wi h
second-o de assessmen ules (Sec ion 3), and discuss possible easons, applica ions, and implica ions
o ou esul s (Sec ion 4).
Games 2017,8, 8 3 o 16
Table 1.
Wha is good and wha is bad? “G” and “B”, espec i ely, desc ibe a good and bad image,
and “C” and “D”, espec i ely, desc ibe o e ing o help and e using o help.
Condi ions Image o ecipien G G B B
Ac ion o dono C D C D
Assessmen ule: Wha
does he dono ’s image
look like?
Shunning (SH) G B B B
S e n judging (SJ) G B B G
Image sco ing (IS) G B G B
Simple s anding (ST) G B G G
2. Ma e ials and Me hods
We will i s conside e olu iona y gi ing games in ini e s uc u ed popula ions. As in he
“spa ial indi ec ecip oca ion” model [
28
], each indi idual plays gi ing games only wi hin a gi en
neighbo hood and upda es his/he own s a egy h ough he pai wise payo compa ison wi h
a andom neighbo . In his s udy, we examine second-o de assessmen ules, as men ioned ea lie .
Condi ional beha io s o each indi idual can hus be in luenced by beha io s o emo e hi d pa ies
ha a e no in he neighbo hood.
2.1. Indi idual-Based Model
Popula ion S uc u e, Indi idual S uc u e, and T ial Sequence
Regula ing la ice.
We conside N= 400 ( ixed) indi iduals. We assume ha all indi iduals a e
placed andomly on nodes o he egula ing la ice (Figu e 1). The numbe o nodes equals ha o
indi iduals, and he e is only one indi idual pe node. The node deg ee o he egula ing la ice is
gi en by an e en numbe kso ha each node connec s o all i s nea es neighbo ing nodes, and he
numbe o he connec ions pe node is k. The connec ions o nodes a e ixed, and he loca ions o
indi iduals a e unchanged h oughou a simula ion ial.
Indi idual s uc u e.
Each indi idual has he ollowing basic a ibu es: {id, loca ion, payo ,
s a egy, sel -image, o he s image lis }. Each indi idual adop s a speci ic s a egy among he h ee
s a egies {Coope a o (ALLC), De ec o (ALLD), Disc imina o (DISC)}. Each indi idual can be
assigned di e en image sco es by o he s because hey may ha e di e en assessmen ules o make
e o s in p i a e assessmen . E e y indi idual will upda e his/he image-lis o all o he indi iduals
in he popula ion [
52
,
53
]. We pa icula ly assume ha sel -image is ixed as “good” and unchanged
h oughou a ial o indi idual-based simula ion.
Simula ion ial.
One ial o he simula ion consis s o g= 500 gene a ions, and each gene a ion
consis s o h= 50 pe iods. In he simula ion ial, he indi idual s a egy is ini ially gi en a andom
om he h ee a ailable: ALLC, ALLD, and DISC. We assume ha , a he beginning o e e y gene a ion,
he image sco es o all indi iduals a e ini ialized as good. In each pe iod, e e y indi idual as a dono
commi s once o a gi ing game in andom o de . Thus, N= 400 game-playe u ns occu pe pe iod.
A he end o e e y gene a ion, all indi iduals synch onously upda e hei own s a egy.
Each game-playe u n comp ises he ollowing h ee phases:
(1)
Playe -selec ion phase.
A ocal playe is selec ed, as a o emen ioned, and is hen o e ed
an oppo uni y o help a ecipien playe , who is andomly selec ed om he ocal playe ’s
closes neighbo hood.
(2)
Gi ing-game phase.
This is a one-sho gi ing game [
7
]. Depending on his/he s a egy
(whose de ails a e gi en la e ), he ocal indi idual de e mines whe he o gi e help o he
ecipien o no . Gi ing help equi es ei he pe sonal cos c> 0 o no hing. Gi ing help means
o play C, and no -gi ing help means o play D. Each helping ac ion leads o bene i s b o he
ecipien wi h b>c. This is a social-dilemma si ua ion: i he in e ac ion is andom ma ching,
i espec i e o wha o he s do, swi ching o playing D is mo e ad an ageous han playing C
Games 2017,8, 8 4 o 16
by sa ing cos s c; ne e heless, he ne payo is 0 i bo h play D and b
−
c> 0 i bo h play C.
We assume implemen a ion e o s, in which he ocal playe who in ends o play C will implemen
D wi h p obabili y pand, simila ly, he ocal playe who in ends o play D will implemen C wi h
p obabili y p. Tha is, he implemen a ion e o is bila e al.
(3)
Image upda ing phase.
Finally, each playe (excep o he ocal playe ) synch onously upda es
his/he own playe -image lis by assessing he ocal playe . We examine wo ex eme moni o ing
scena ios: e e y gi ing game is moni o ed by (i) a ep esen a i e obse e wi h a p ope
assessmen ule (indi ec obse a ion) o (ii) all playe s (excep o he ocal playe ) (di ec
obse a ion) [
54
]. In (i) indi ec obse a ion, he ep esen a i e obse e assesses he ocal
playe , elying on he ocal playe ’s las ac ion in he gi ing game and he ecipien ’s image.
We assume assessmen e o s: in making assessmen s, he ep esen a i e obse e makes e o s
wi h p obabili y q, in which he ep esen a i e obse e assigns a good image o hose who, in he
case wi h no assessmen e o , should ha e a bad one o a bad image o hose who, in he case wi h
no assessmen e o , should ha e a good one. Hence, he assessmen e o is bila e al. The same
assessmen in o ma ion ega ding he ocal playe is hen sha ed by all indi iduals, whe he
ha in o ma ion is e oneous o no [
8
,
9
]. In (ii) di ec obse a ion, all obse ing indi iduals
independen ly assess he ocal playe , and each indi idual independen ly commi s o assessmen
e o s wi h p obabili y q[
55
], as is assumed o he ep esen a i e indi idual in (i). In his s udy,
we do no conside any speci ic consensus o ma ion among indi iduals.
S a egy upda ing and mu a ion.
We assume ha all indi iduals unde go p obabilis ic s a egy
upda ing and a e mu a ion synch onously a he end o e e y gene a ion. Fo s a egy upda ing,
he model indi idual is andomly chosen among he closes neighbo s o he ocal indi idual. As wi h
eplica o dynamics in well-mixed popula ions [
56
], we conside he selec ion, which depends on he
payo di e ence be ween he wo. Le
Pi
be he accumula ed payo o indi idual i h oughou he las
gene a ion. The p obabili y o a ocal indi idual i o selec he model j’s s a egy is de ined as:
P (i→j)=1/1+exp−sPj−Pi (1)
The ocal indi idual hen unde goes mu a ion wi h p obabili y mand, i so, he ocal indi idual
will andomly swi ch o one o he gi en h ee s a egies.
2.2. Game S a egies and Assessmen Rules
To in es iga e he e ec s o di e en assessmen ules on he eme gence o indi ec ecip oci y in
social ne wo ks, we conside he ollowing ypical s a egies:
•De ec o (ALLD): playing D uncondi ionally
•Coope a o (ALLC): playing C uncondi ionally
•
Disc imina o (DISC): playing C (i he ecipien has a good image) o playing D (i he ecipien
has a good image)
We assume ha , in he beginning o indi idual-based simula ion, each node o he egula
ing la ice is occupied wi h a s a egis ha is andomly selec ed om he abo e h ee, unless
o he wise ins uc ed.
Who is good o bad is de e mined by he assessmen ule. In his pape , we examine he ou
assessmen ules, as ollows (see also Table 1):
•
Shunning (SH): ei he assessing a dono as good i he dono plays C o a ecipien who has a good
image o assessing he dono as bad. Shunning is he s ic es among he ou ules [50].
•
Image sco ing (IS): ei he assessing a dono as good i he dono plays C o assessing a dono as
bad i he dono plays D o a ecipien , i espec i e o he ecipien ’s image. Image sco ing is he
simples among he ou ules because i depends only on he dono ’s ac ion [40].

Games 2017,8, 8 5 o 16
•
S e n judging (SJ): assessing a dono as good i he dono ei he plays C o a ecipien who has
a good image o plays D o a ecipien who has a bad image. S e n judging is he second s ic es
assessmen ule because a playe who has a bad image can also cleanse ha image by e using
o help ano he playe who has a bad image [
48
,
49
]. This assessmen o de ec ion is a so-called
“jus i ied de ec ion” [3]. S e n judging is one o he eigh leading ules [8,9].
•
Simple s anding (SS): ei he assessing a dono as bad i he dono plays D o a ecipien who has
a bad image o assessing a dono as good [
3
,
46
,
47
]. Simple s anding is he mos ole an among
he ou ules and is also one o he eigh leading ules.
Figu e 1shows an example o a se ies o game in e ac ions and image assessmen s.
Games2017,8,8 5o 16
assessmen  ulebecauseaplaye whohasabadimagecanalsocleanse ha imageby e using
ohelpano he playe whohasabadimage[48,49].Thisassessmen o de ec ionisaso‐called
“jus i iedde ec ion”[3].S e njudgingisoneo  heeigh leading ules[8,9].
 Simples anding(SS):ei he assessingadono asbadi  hedono playsD oa ecipien whohas
abadimageo assessingadono asgood[3,46,47].Simples andingis hemos  ole an among
he ou  ulesandisalsooneo  heeigh leading ules.
Figu e1showsanexampleo ase ieso gamein e ac ionsandimageassessmen s.

Figu e1.Ac ionsandassessmen sin hegi inggamesina egula ne wo kwi hapopula ionsizeo 
8andanodedeg eeo 4.Weassume ha indi idualsX,Y,Z,andWin hene wo kabo ea eall
Disc imina o s;X,Y,andZadop  hesimples anding uleand,ini ially,Whasagoodimageunde 
simples anding.Theo de o playisas ollows: i s ,Z(dono ) oW( ecipien ),second,Y oZ,and
hi d,X oY.I will ollow ha , i s ,Zin ends ocoope a e,andweassume ha Ze oneously
de ec s oW.Thus, heimageo Zbecomesbad om he iewpoin o ST.Second,Ywillde ec  oZ;
hus,X’simageo Ywillbecomegood.Finally,Xwillcoope a ewi hY.
3.Resul s
InFigu es2and3,wenume icallycalcula e he a eo  hecoope a ionac ionCo e allac ions
ascon ollingbene i sb,nodedeg eesk,andwhe he assessmen e o sa epublico p i a e.In
Figu es4and5,wein es iga e hee olu iono spa ialpa e nswi hdi e en assessmen  ules.
Finally,inFigu e6,wecompa e he esul s ega ding hesec ionwi hb=5.
3.1.In heAbsenceo Indi ec Recip oci y
Fo  e e ence,wes a byin es iga inghow he egula  ingla icei sel cana ec  hee olu ion
o coope a ionin hegi inggame.Weconside only heCoope a o (ALLC)andDe ec o (ALLD).
Weconduc indi idual‐basedsimula ionsinwhichin heini ialse ingo eachnodes a egyon he
g aphisselec ed andomlybe ween heALLCand heALLD,ando he pa ame e sa e hesameas
inFigu es2and3.Thisin es iga ionisindependen o  hequali yo assessmen e o sbecauseno
s a egy ha dependson epu a ionassessmen isassumed.We ind ha  hespa ials uc u ecan
onlymain aincoope a iona a e ylow a e(suchas hemu a ion a e)unde  he ypicalpa ame e 
se ings.Noclus e o coope a ione ol es o anydeg eeo k.Thisindica es ha  hespa ial
s uc u ei sel wouldha enoe ec on hee olu iono coope a ionin hegi inggame.
Figu e 1.
Ac ions and assessmen s in he gi ing games in a egula ne wo k wi h a popula ion size
o 8 and a node deg ee o 4. We assume ha indi iduals X, Y, Z, and W in he ne wo k abo e a e all
Disc imina o s; X, Y, and Z adop he simple s anding ule and, ini ially, W has a good image unde
simple s anding. The o de o play is as ollows: i s , Z (dono ) o W ( ecipien ), second, Y o Z,
and hi d, X o Y. I will ollow ha , i s , Z in ends o coope a e, and we assume ha Z e oneously
de ec s o W. Thus, he image o Z becomes bad om he iewpoin o ST. Second, Y will de ec o Z;
hus, X’s image o Y will become good. Finally, X will coope a e wi h Y.
3. Resul s
In Figu es 2and 3, we nume ically calcula e he a e o he coope a ion ac ion C o e all
ac ions as con olling bene i s b, node deg ees k, and whe he assessmen e o s a e public o p i a e.
In
Figu es 4and 5,
we in es iga e he e olu ion o spa ial pa e ns wi h di e en assessmen ules.
Finally, in Figu e 6, we compa e he esul s ega ding he sec ion wi h b= 5.
3.1. In he Absence o Indi ec Recip oci y
Fo e e ence, we s a by in es iga ing how he egula ing la ice i sel can a ec he e olu ion
o coope a ion in he gi ing game. We conside only he Coope a o (ALLC) and De ec o (ALLD).
We conduc indi idual-based simula ions in which in he ini ial se ing o each node s a egy on he
g aph is selec ed andomly be ween he ALLC and he ALLD, and o he pa ame e s a e he same as
in Figu es 2and 3. This in es iga ion is independen o he quali y o assessmen e o s because no
s a egy ha depends on epu a ion assessmen is assumed. We ind ha he spa ial s uc u e can
only main ain coope a ion a a e y low a e (such as he mu a ion a e) unde he ypical pa ame e
se ings. No clus e o coope a ion e ol es o any deg ee o k. This indica es ha he spa ial s uc u e
i sel would ha e no e ec on he e olu ion o coope a ion in he gi ing game.
Games 2017,8, 8 6 o 16
3.2. Public Assessmen
Figu e 2shows he esul s o indi ec obse a ion and public assessmen e o s. The esul s e eal
ha , among he ou ules (shunning, image sco ing, s e n judging, and simple s anding), s e n judging
and simple s anding a e mos likely o p omo e coope a ion and dominance by Disc imina o s. Simila
o each o he , and as he node deg ee o he ne wo k dec eases, he h eshold deg ee o b, ac oss
which s e n judging o simple s anding can lead o a ull coope a ion a e and Disc imina o equency,
will inc ease. In s e n judging and simple s anding, spa se ne wo ks a e mo e likely o acili a e he
es ablishmen o a p osocial s a e han dense ne wo ks.
In shunning, depending on he speci ic pa ame e se ings, Disc imina o s can a ain highe
ela i e equencies han in ei he s e n judging o simple s anding. Howe e , his does no ca y ull
coope a ion ( he coope a ion a e is 0.6 a mos in Figu e 2A).
The coope a ion a e in image sco ing inc eases a a mo e g adual a e han in shunning because
i eaches i s maximum a a high bene i band middle node deg ee k(abou 0.8, as shown in Figu e 2B);
addi ionally, he Disc imina o equency only akes he in e media e alue and hus does no mo e in
co ela ion. I is obse ed ha he Disc imina o , ALLC, and ALLD can dynamically coexis wi hin he
ne wo k a non-la ge node deg ees (Figu e 4B). Pa icula ly a low deg ees o k, cyclical eplacemen
occu s among he h ee s a egies.
To be e unde s and hese phenomena in image sco ing, we conduc ex a simula ions o bo h
he Disc imina o and he ALLD. These ials e eal ha conside ing only he Disc imina o and he
ALLD leads he Disc imina o o ake o e he en i e popula ion; howe e , he e is an in e media e
coope a ion a e, which is independen o he node deg ee k, as in shunning. We no e ha bo h he
Disc imina o and he ALLC can achie e a highe coope a ion a e in combina ion han in isola ion on
he egula ing la ice wi h a low node deg ee. Di e en ly om he o he h ee ules, image sco ing
canno su i e high node deg ees in which popula ion ne wo ks a e highly dense. This is consis en
wi h he esul s om he eplica o dynamics o an in ini e, well-mixed popula ion [54].
Games2017,8,8 6o 16
3.2.PublicAssessmen 
Figu e2shows he esul so indi ec obse a ionandpublicassessmen e o s.The esul s
e eal ha ,among he ou  ules(shunning,imagesco ing,s e njudging,andsimples anding),
s e njudgingandsimples andinga emos likely op omo ecoope a ionanddominanceby
Disc imina o s.Simila  oeacho he ,andas henodedeg eeo  hene wo kdec eases, he h eshold
deg eeo b,ac osswhichs e njudgingo simples andingcanlead oa ullcoope a ion a eand
Disc imina o  equency,willinc ease.Ins e njudgingandsimples anding,spa sene wo ksa e
mo elikely o acili a e hees ablishmen o ap osocials a e handensene wo ks.
Inshunning,dependingon hespeci icpa ame e se ings,Disc imina o scana ainhighe 
ela i e equencies haninei he s e njudgingo simples anding.Howe e , hisdoesno ca y ull
coope a ion( hecoope a ion a eis0.6a mos inFigu e2A).
Thecoope a ion a einimagesco inginc easesa amo eg adual a e haninshunning
becausei  eachesi smaximuma ahighbene i bandmiddlenodedeg eek(abou 0.8,asshownin
Figu e2B);addi ionally, heDisc imina o  equencyonly akes hein e media e alueand hus
doesno mo einco ela ion.I isobse ed ha  heDisc imina o ,ALLC,andALLDcan
dynamicallycoexis wi hin hene wo ka non‐la genodedeg ees(Figu e4B).Pa icula lya low
deg eeso k,cyclical eplacemen occu samong he h ees a egies.
Tobe e unde s and hesephenomenainimagesco ing,weconduc ex asimula ions o bo h
heDisc imina o and heALLD.These ials e eal ha conside ingonly heDisc imina o and he
ALLDleads heDisc imina o  o akeo e  heen i epopula ion;howe e , he eisanin e media e
coope a ion a e,whichisindependen o  henodedeg eek,asinshunning.Weno e ha bo h he
Disc imina o and heALLCcanachie eahighe coope a ion a eincombina ion haninisola ion
on he egula  ingla icewi halownodedeg ee.Di e en ly om heo he  h ee ules,image
sco ingcanno su i ehighnodedeg eesinwhichpopula ionne wo ksa ehighlydense.Thisis
consis en wi h he esul s om he eplica o dynamicso anin ini e,well‐mixedpopula ion[54].

Figu e2.Coope a ion a esandDisc imina o  equenciesinindi ec obse a ionandpublic
assessmen e o s.(A)Shunningcan akeo e  heen i epopula ionye achie e,a mos ,an
in e media ecoope a ion a e;(C,D)bo hs e njudgingandsimples andingcana ain ull
coope a ioninas a eo almos  ullDisc imina o s o la gebene i sb;(B)imagesco ingcan
main ainahighcoope a ion a ewi hDisc imina o swhose equenciesa eless hanhal .
Pa ame e s:g=500gene a ions,h=50pe iods,e o  a esp=q=0.01(bo h o implemen a ionand
publicassessmen e o s),selec ionin ensi ys=1,mu a ion a em=0.01,nodedeg ees={2,4,8,16,
Figu e 2.
Coope a ion a es and Disc imina o equencies in indi ec obse a ion and public
assessmen e o s. (
A
) Shunning can ake o e he en i e popula ion ye achie e, a mos ,
an in e media e coope a ion a e; (
C
,
D
) bo h s e n judging and simple s anding can a ain ull
coope a ion in a s a e o almos ull Disc imina o s o la ge bene i s b; (
B
) image sco ing can
main ain a high coope a ion a e wi h Disc imina o s whose equencies a e less han hal . Pa ame e s:
g= 500 gene a ions
,h= 50 pe iods, e o a es p=q= 0.01 (bo h o implemen a ion and public
assessmen e o s), selec ion in ensi y s= 1, mu a ion a e m= 0.01, node deg ees = {2, 4, 8, 16, 32,
64, 100, 150, 200, 250, 300, 350, and 400}, c= 1, and 1
≤
b
≤
5 (a in e al 0.2). The coope a ion a es
and Disc imina o equencies depic ed a e he a e ages calcula ed o e 20 independen uns o he
agen -based simula ion.
Games 2017,8, 8 7 o 16
3.3. P i a e Assessmen
Figu e 3shows he esul s o he di ec obse a ion and p i a e assessmen e o s. The quali a i e
changes in e o s ha e li le e ec on he esul ing coope a ion a es in simple s anding and image
sco ing. Howe e , his is no he case o shunning and s e n judging. The ho izon al su ace o he
maximal coope a ion a e in shunning d as ically d ops o 0.2 in Figu e 3B. The coope a ion a e in
s e n judging su e s u he ca as ophic damage, dec easing all he way o ze o and esul ing in
bene i s bo high node deg ees kin Figu e 3C. In simula ions wi h a longe pe iod pe gene a ion,
he coope a ion a es in bo h shunning and s e n judging u he decline o ze o in Figu e 6B.
Games2017,8,8 7o 16
32,64,100,150,200,250,300,350,and400},c=1,and1≤b≤5(a in e al0.2).Thecoope a ion a es
andDisc imina o  equenciesdepic eda e hea e agescalcula edo e 20independen  unso  he
agen ‐basedsimula ion.
3.3.P i a eAssessmen 
Figu e3shows he esul so  hedi ec obse a ionandp i a eassessmen e o s.The
quali a i echangesine o sha eli lee ec on he esul ingcoope a ion a esinsimples anding
andimagesco ing.Howe e , hisisno  hecase o shunningands e njudging.Theho izon al
su aceo  hemaximalcoope a ion a einshunningd as icallyd ops o0.2inFigu e3B.The
coope a ion a eins e njudgingsu e s u he ca as ophicdamage,dec easingall heway oze o
and esul inginbene i sbo highnodedeg eeskinFigu e3C.Insimula ionswi halonge pe iod
pe gene a ion, hecoope a ion a esinbo hshunningands e njudging u he decline oze oin
Figu e6B.

Figu e3.Coope a ion a esandDisc imina o  equenciesindi ec obse a ionandp i a e
assessmen e o s.(A)Shunningcan akeo e  heen i epopula ionye onlyachie e,a mos ,alow
coope a ion a e;(C)s e njudgingcanachie ealmos  ullcoope a ion,ascanDisc imina o 
equencyi ,andonlyi ,bene i sbandnodedeg eeska esu icien lyhighandlow, espec i ely;
o he wise,bo h hecoope a ion a eand heDisc imina o  equency educe oze o;(D)simple
s andingcanachie e ullcoope a ionand100%Disc imina o s o ab oad angeo pa ame e s,as
showninFigu e2D;(B)imagesco ingcanmain ainahighcoope a ion a einamixeds a ewi h
Coope a o sandDisc imina o s(seealsoFigu e5B).Pa ame e s:e o  a esp=q=0.01(bo h o 
implemen a ionandp i a eassessmen e o s)ando he pa ame e sa eshowninFigu e2.
3.4.E olu iono Spa ialPa e ns
Wi hnoindi ec  ecip oci ymechanism,Coope a o scanno su i eby hemsel esin he
p esenceo De ec o son he egula  ingla ice(Sec ion3.1).Figu es4and5show ypical
e olu iona ypa e nso spa ialindi ec  ecip oci yon he egula  ingla ice, espec i ely,wi h
publicandassessmen e o s.Fo  helowes nodedeg ee2,cycleso Disc imina o s(DISCs),
Coope a o s(ALLCs)(bluecolo ),andDe ec o s(ALLDs)(blackcolo )a eobse ed h oughou all
ou  ules.Wi hindi ec obse a ionandpublicassessmen e o s(Figu e4),shunning(SH)( ed
colo )ismos likely odomina e hepopula ionamong he ou  ules;howe e , hecoope a ion
le elisno high.S e njudging(SJ)islikely odomina easwell.No ably, hese esul sa eno  obus 
ega dingchangingwi hin hiskindo assessmen e o .Wi hdi ec obse a ionandp i a e
Figu e 3.
Coope a ion a es and Disc imina o equencies in di ec obse a ion and p i a e assessmen
e o s. (
A
) Shunning can ake o e he en i e popula ion ye only achie e, a mos , a low coope a ion
a e; (
C
) s e n judging can achie e almos ull coope a ion, as can Disc imina o equency i , and only i ,
bene i s band node deg ees ka e su icien ly high and low, espec i ely; o he wise, bo h he coope a ion
a e and he Disc imina o equency educe o ze o; (
D
) simple s anding can achie e ull coope a ion
and 100% Disc imina o s o a b oad ange o pa ame e s, as shown in Figu e 2D; (
B
) image sco ing
can main ain a high coope a ion a e in a mixed s a e wi h Coope a o s and Disc imina o s (see also
Figu e 5B). Pa ame e s: e o a es p=q= 0.01 (bo h o implemen a ion and p i a e assessmen e o s)
and o he pa ame e s a e shown in Figu e 2.
3.4. E olu ion o Spa ial Pa e ns
Wi h no indi ec ecip oci y mechanism, Coope a o s canno su i e by hemsel es in he p esence
o De ec o s on he egula ing la ice (Sec ion 3.1). Figu es 4and 5show ypical e olu iona y pa e ns
o spa ial indi ec ecip oci y on he egula ing la ice, espec i ely, wi h public and assessmen e o s.
Fo he lowes node deg ee 2, cycles o Disc imina o s (DISCs), Coope a o s (ALLCs) (blue colo ),
and De ec o s (ALLDs) (black colo ) a e obse ed h oughou all ou ules. Wi h indi ec obse a ion
and public assessmen e o s (Figu e 4), shunning (SH) ( ed colo ) is mos likely o domina e he
popula ion among he ou ules; howe e , he coope a ion le el is no high. S e n judging (SJ) is
likely o domina e as well. No ably, hese esul s a e no obus ega ding changing wi hin his kind
o assessmen e o . Wi h di ec obse a ion and p i a e assessmen e o s (Figu e 5), shunning
leads o a low coope a ion a e, and s e n judging can esul in bo h a low coope a ion a e and
Disc imina o equency. Compa ed wi h shunning and s e n judging, he esul s om image sco ing
and simple s anding a e mo e obus o changes in bo h public and p i a e cases. Image sco ing (IS)
Games 2017,8, 8 8 o 16
is mo e likely o subsis han s e n judging because, in o ming clus e s, i su i es h ough a dynamic
coexis ence wi h ALLCs and ALLDs. The ALLD clus e is eplaced wi h he Disc imina o clus e ;
he Disc imina o clus e will hen be eplaced wi h he ALLC clus e ; he ALLC clus e will hen
be eplaced wi h he ALLD clus e . Fo in e media e alues o b and k, only image sco ing can lead
o a “ ock-pape -scisso s” ype o dynamic. This yields a highe coope a ion a e han ha o he
homogeneous s a es o Disc imina o s. When he node deg ee inc eases, he a e age equency and
clus e size o he Disc imina o dec eases. Fo la ge bene i s b and la ge node deg ees k, bo h he
Disc imina o and ALLC clus e s can become ine , which can achie e he highes coope a ion a e.
Simple s anding (ST) can main ain clus e s o Disc imina o s o long pe iods, which can some imes
be eplaced wi h ALLCs bu no wi h ALLDs.
Games2017,8,8 8o 16
assessmen e o s(Figu e5),shunningleads oalowcoope a ion a e,ands e njudgingcan esul 
inbo halowcoope a ion a eandDisc imina o  equency.Compa edwi hshunningands e n
judging, he esul s omimagesco ingandsimples andinga emo e obus  o changesinbo h
publicandp i a ecases.Imagesco ing(IS)ismo elikely osubsis  hans e njudgingbecause,in
o mingclus e s,i su i es h oughadynamiccoexis encewi hALLCsandALLDs.TheALLD
clus e is eplacedwi h heDisc imina o clus e ; heDisc imina o clus e will henbe eplaced
wi h heALLCclus e ; heALLCclus e will henbe eplacedwi h heALLDclus e .Fo 
in e media e alueso bandk,onlyimagesco ingcanlead oa“ ock‐pape ‐scisso s” ypeo 
dynamic.Thisyieldsahighe coope a ion a e han ha o  hehomogeneouss a eso 
Disc imina o s.When henodedeg eeinc eases, hea e age equencyandclus e sizeo  he
Disc imina o dec eases.Fo la ge bene i sbandla ge nodedeg eesk,bo h heDisc imina o and
ALLCclus e scanbecome ine ,whichcanachie e hehighes coope a ion a e.Simples anding
(ST)canmain ainclus e so Disc imina o s o longpe iods,whichcansome imesbe eplacedwi h
ALLCsbu no wi hALLDs.

Figu e4.E olu iono spa ialpa e nso indi ec  ecip oci yon egula  ingla iceswi hindi ec 
obse a ionandpublicassessmen e o s.(A)Shunning(SH)( edcolo )and(C)s e njudging(SJ)
(o angecolo )a elikely o akeo e  hepopula ion.SJcanalsoachie ealmos  ullcoope a ion;ye ,
inSH, hecoope a ion a eislow;(B)imagesco ing(IS)(yellowcolo )ismos likely olead oa
h ee‐s a egydynamicalcoexis ence,inwhichcase, hes a egyisadop edbyeachnodechange
equen ly.Asinc easesa eseeninbene i bandnodedeg eek, hea e ageclus e sizeo IS
Figu e 4.
E olu ion o spa ial pa e ns o indi ec ecip oci y on egula ing la ices wi h indi ec
obse a ion and public assessmen e o s. (
A
) Shunning (SH) ( ed colo ) and (
C
) s e n judging (SJ)
(o ange colo ) a e likely o ake o e he popula ion. SJ can also achie e almos ull coope a ion;
ye , in SH, he coope a ion a e is low; (
B
) image sco ing (IS) (yellow colo ) is mos likely o lead o
a h ee-s a egy dynamical coexis ence, in which case, he s a egy is adop ed by each node change
equen ly. As inc eases a e seen in bene i band node deg ee k, he a e age clus e size o IS dec eases,
becoming eplaced wi h an ALLC; (
D
) simple s anding (ST) (cyan colo ) is mos likely o main ain
a s a e ha is exclusi ely mixed wi h DISCs and ALLCs. Pa ame e s: g= 500 gene a ions, h= 50
pe iods, e o a es p=q= 0.01 (bo h o implemen a ion and public assessmen e o s), selec ion
in ensi y s= 1, mu a ion a e m= 0.01, and c= 1.
Games 2017,8, 8 15 o 16
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