1
Cen alizing in o ma ion imp o es ma ke e iciency
mo e han inc easing in o ma ion:
Resul s om expe imen al asse ma ke s*
I án Ba eda-Ta azonaa,
1
, Gianluca G imaldaa, c,
And ea Mo one a, b, Simone Nuzzob, And ea Teglioa
aLEE & Economics Depa men , Uni e si a Jaume I, Cas ellón, Spain
b Dipa imen o di Economia, Managemen e Di i o d’imp esa, Uni e si à degli S udi di Ba i, Aldo
Mo o, I aly
c Ins i u ü Wel wi scha , Kiel, Ge many
Abs ac
We s udy he ela ionship be ween ma ke e iciency and he dis ibu ion o p i a e in o ma ion in
expe imen al inancial asse ma ke s. T ade s ecei e impe ec signals o e he eal alue o an asse .
Agen s can sha e hei in o ma ion wi hin a ela i ely small – compa ed o ma ke size - g oup o
agen s. Bo h he numbe o signals and he way hese a e alloca ed among agen s a e manipula ed in
ou expe imen al ea men s. In wo ea men s signals a e e enly dis ibu ed among agen s. In wo
o he ea men s one g oup o ‘quasi-inside ’ agen s ecei es mo e signals han all o he g oups. In he
baseline condi ion no signal is dis ibu ed. We show ha cen alizing in o ma ion unambiguously
achie es highe ma ke e iciency han sp eading in o ma ion e enly. Fu he mo e, inc easing he
amoun o in o ma ion has no e ec on e iciency ei he when in o ma ion is symme ic o when i is
asymme ic. We a gue ha wo complemen a y mechanisms d i e hese esul s. Fi s , ha ing mo e
p i a e in o ma ion ex an e induces ade s o ely on hei own signals, educing he expec ed bene i s
o sha ing in o ma ion. Second, he p esence o quasi-inside being common knowledge p omp s
agen s o ex ac mo e in o ma ion om ma ke p ices a he han hei own p i a e signals. This leads
o swi in o ma ion agg ega ion.
Key wo ds: Expe imen al Ma ke s; In o ma ion Agg ega ion; Ma ke Coope a ion
* Financial suppo by Uni e si a Jaume I (p ojec P1.1B2015-48) and he Spanish Minis y o Economics and
Compe i i eness (p ojec s ECO2013-44409-P and ECO2015-68469-R) is g a e ully acknowledged.
1
Co esponding au ho : LEE & Economics Depa men , Uni e si a Jaume I, 12071 Cas ellón, Spain. E-mail
add ess: i an.ba [email protected].
2
In oduc ion
The capaci y o ma ke s o e icien ly agg e ga e p i a ely dispe sed in o ma ion has
been a cen al opic in economics since Adam Smi h and on Hayek. In he con ex o
inancial ma ke s, Fama (1965) de ines a ma ke as e icien whene e p ices " ully
e eal" he in o ma ion dispe sed in he ma ke . In ui i ely, e iciency can be achie ed
becau se ade s owning p i a e in o ma ion on he eal alue o an asse – so-called
“inside s” - will seek o p o i whene e p ices do no ully embody hei own p i a e
in o ma ion. I ma ke s a e e icien , inside s’ p i a e i n o ma ion is in he long un
wo hless and inside s canno ealize highe gains han o he ade s. In he sho un,
unin o med ade s can y o in e he exis ence o inside in o ma ion om he
obse a ion o ading ac i i y, in o de o also ealize p o i s. This can ei he accele a e
he p ocess o con e gence owa d he equi lib ium, o d i e i as ay i unin o med
ade s a e mis aken i n hei in e ences, as he li e a u e on in o ma ional cascades
demons a es (Bikhchandani e al., 1998).
The expe imen al li e a u e has ex ensi ely examine d he condi ions a which
inancial ma ke s achie e e iciency (see he nex sec ion o a e iew). Howe e , his is
no mally done in se ings whe e agen s a e ei he ully in o med o no in o med, and
ha e no connec ions wi h o he s. In his pape we gene alize on bo h o hese
condi ions. We allow o all agen s o ha e impe ec in o ma ion and o some agen s
– whom we call “quasi-inside s” - o ha e close- o-pe ec in o ma ion. We a y he
o e all amoun o in o ma ion a ailable in he ma ke an d he way his is dis ibu ed
among agen s. In pa icula , in a wo-by- wo desi gn, i n o ma ion is ei he equally
dis ibu ed among ade s o is unequally dis ibu ed. In he la e case, “quasi-inside s”
ecei e a highe amoun o in o ma ion han o he agen s. Mo eo e , he o e all
quan i y o in o ma ion is also modi ied ac oss ou expe imen al condi ions.
Secondly, we in oduce a simple ne wo k s uc u e in ou inancial ma ke s. Each
agen is connec ed wi h wo o he agen s and each has he op ion o sha e hei own
p i a e in o ma ion wi h he wo o he agen s i n hei g oup. The impo ance o
ne wo ks in inancial ma ke s has been s essed bo h he o e ically and empi ically.
Acco ding o Abou la ia, (1997), inancial ma ke s a e embedded in o a as and dense
ne wo k o cus oma y codes o conduc s, mu ual expec a ion s o app op ia e beha io ,
and us among i ndi idual agen s. In ac , some accoun s s ess ha he b eakdown in
he ne wo ks o us among inancial agen s played a majo ole in p ecipi a ing a nd
3
agg a a ing he 2008 inancial c isis (Ki man, 2010; Anand e al., 2013). Acco ding o
his iew, inancial ma ke s may sha e some cha ac e is ics wi h s anda d ma ke s o
goods, whe e social no ms and us ne wo ks can ca use he ac ual ma ke p ice o
depa om he Wal a sian p ice (G ei , 1993). The e ec o us ne wo k in inancial
ma ke s is a la gely unexplo ed issue. We a e he i s , o he bes o ou knowledge, o
examine i expe imen ally. Ou main esea ch ques ion is whe he and how he
amoun , dis ibu ion, and he sp eading o in o ma io n h ough he ne wo k, i nc ease
ma ke e i ciency.
Excep o he baseline c ondi ion whe e no a gen ecei es any in o ma ion, in all
o he expe imen al condi ions all agen s ecei e some noisy signals on he undamen al
alu e o he asse . Such signals only e eal he eal alue o he asse wi h 70%
p ob abili y. We conside wo cases whe e each agen is ei he alloca ed he same
numbe o signals as all o h e s o whe e some “q uasi-inside s” a e endowed wi h a
la ge numbe o signals. The o e all numbe o signals dis ibu ed in he m a ke be o e
an sac ions i s also manip ula ed ac oss expe imen al condi ions.
Ou amewo k enables us o s udy wo di e en mechanisms o he di usion o
in o ma ion in he ma ke . The i s is wha we call a “leade ship mechanism”, whe e i
is common knowledge ha one g oup o quasi-inside s wi hin he ma ke owns ex an e
mo e in o ma i e signals han all o he g oups. In some cases quasi-inside s can expec
o know he eal alue o he asse wi h p obabili y g ea e han 95%
2
. We expec ha
his mechanism will ha e impo an consequences on “in o ma ion di sclosu e” (see
nex sec ion) and hus on ma ke e iciency. On he one ha nd, quasi-inside s will
p esumably y o gain om hei in o ma ional ad an age, and hei ading ac i i y
should, ce e is pa ibus, d i e he asse p ice in he di ec ion o he undamen al alue
as e han i n o he cases. On he o he hand, les s in o med ade s may pay mo e
a en ion o he p ice adjus men s wi hin h e ma ke , because he p esence o quasi-
inside s should make hem awa e o he possi bili y ha p ices mo e in he di ec ion o
he undamen al as e han in o he cases.
The second channel is wha we call a “coope a ion mechanism”, whe eby agen s
can sha e hei p i a e signal(s) wi hin g oups o med by h ee membe s, a nd can in
2
The e m “inside ” no mally ch a ac e izes ade s who know wi h p o babili y one he eal alue o he
asse . S ince in ou s udy ade s h a ing in o ma ional ad an age can ne e be absolu ely ce ain o he
eal alue o he asse , we p e e o call h em “quasi-inside s”. See also sec ion 2.
4
u n ecei e he in o ma ion sha ed by he o he wo membe s o hei g oup. This is
done be o e ading s a s, so agen s can access he ma ke wi h a la ge numbe o pe
capi a signals, i o he s in hei g oup ha e decided o sha e. In he coope a ion
mechanism, in o ma ion is he e o e mul iplied i agen s decide o sha e. I coope a ion
does occu , we expec ha ansac ions will become mo e in o ma i e and, in agg ega e,
p ices may inco po a e he a ailable i n o ma ion. Manipula ing he quan i y o signals
owned by quasi-inside s makes i possible o specula e o e he ela i e s eng h o
hese wo ac o s.
Ou expe imen al design includes a baseline condi ion whe e no in o ma ion is
a ailable o agen s, and ou ea men condi ions ha a y bo h he amoun and he
concen a ion o signals. In o ma ion is e enly dis ibu ed among agen s in wo o such
ea men s,, bu he o al numbe o signals is ipled in one ea men compa ed o he
o he . Tha is, in one ea men each agen ecei es one signal, while in he o he
ea men each agen ecei es h ee signals. In wo o he condi ions in o ma ion is
une enly dis ibu ed be ween one g oup o quasi-inside s and h ee g oups o non-
inside s. In hese wo condi ions he o al numbe o si gnals is kep cons an . This
enables us o e alua e he impac on e iciency o modi ying he dis ibu ion o signals
om e en o une en.
In o de o be e app ecia e he ele ance o each o he wo mechanisms
illus a ed abo e, we d aw on wo di e en p ice benchma ks. The i s is he “Bayesian
p ice”. This is he p ice ha would esul i all ade s agg ega ed he in o ma ion a
hei disposal a ionally – namely, acco ding o he Bayes ule – a e ade s ha e
decided whe he o sh a e hei signals wi hin hei g oup o no . Mo e p ecisely,
indi idual Bayesian p ices a e compu ed o each ade , and he ma ke Bayesian p ice
is calcula ed as he a i hme ic mean o such indi idual p ices. The second no ion is
wha we call “Fama-ma ke e iciency”, and d aws on he idea se ou a he beginning
o he pape ha p ices should inc o po a e all he in o ma ion p esen in he ma ke .
Fo Fama-e iciency we do no conside signals being sha ed in he “ coope a ion s a ge”,
bu we only conside he in o ma ion a ailable be o e such a s age. He e we compu e
wha we call he “Fama-e icien ” p ice as ha esul ing om he assump ion ha each
agen knew he whole in o ma ion p esen in he ma ke .
We ind ha he “leade ship mechanism” unambiguously b ings abou mo e
e iciency han he "coope a ion mechanism”. In e es ingly, we a lso ind ha inc easing
5
he quan i y o signals does no necessa ily lead o app eciable gains in e iciency. In
pa icula , e iciency is no highe in he symme ic ea men ha ing h ice as many
signals as he al e na i e symme ic ea men . Likewise, e icie ncy is no highe in he
asymme ic ea men h a ing o e all wice as many signals as he al e na i e
asymme ic ea men . None heless, he wo asymme ic ea men s b ing abou
app eciably mo e e ici ency han he symme ic ones. We specula e ha he main
d i e o hi s esul is non-inside s ex ac ing in o ma ion om ma ke p ices mo e
ac i ely han in symme ic ea men s.
Ou s udy is o in e es o he heo e ical issue o whe he ma ke s a e capable
o e icien ly agg ega ing and dissemina ing p i a e in o ma ion. We inno a e on
p e ious li e a u e (see n ex sec ion) by gene a lizing he s anda d a mewo k in he
wo di ec ions men ioned abo e. Tha is, we allow o all agen s o ecei e impe ec
signals, compa ing cases o equal dis ibu ion o he in o ma ion and unequal
dis ibu ion. We also in oduce a ne wo k s uc u e whe eby agen s can sha e hei
p i a e in o ma ion. We belie e ha ou s udy is al so ele an o policy issues.
In es iga ing how ma ke e iciency is a ec ed by inc easing in o ma ion o sp eading
i mo e e enly, and how in o ma ion sp eads wi hin ne wo ks, a e all impo an
ques ions o he op imal managemen o inancial ma ke s. Bo h in no mal imes bu ,
e en mo e so, in imes o “c isis”, inancial au ho i ies may decide o elease addi ional
pieces o in o ma ion o s abilize ma ke s. Ou expe imen al e ide nce may help
unde s and how o do his op imally.
The emain de o he pape is o ganized as ollows. I n he nex sec ion we p esen
a e iew o ele an li e a u e and in he hi d sec ion he expe imen al design. In
sec ion 4 we p esen he me hodology o he analysi s, hen in sec ion 5 we epo he
esul s ob ained. Sec ions 6 discu sses he esul s and 7 conclude.
2 Rela ed Li e a u e
Expe imen al s udie s dealing wi h in o ma ional e iciency a e ypically di ided in o
h ee ypes. The i s one is he dissemina ion o in o ma ion om iden ically in o med
agen s - no mally e e ed o as “inside s” - o unin o med ade s (Plo and Sunde ,
1982). The second s and includes s udies abou in o ma ion agg ega ion among
ma ke pa icipan s wi h less han pe ec i n o ma ion (Plo and Sunde , 1988). The
hi d on e ocuses on h e simul aneous equilib ium in asse and in o ma i on ma ke s

6
(Sunde , 1992). Theo e ically, he i n o ma ion agg ega ion p ocess can be expec ed o
be mo e sluggish in achie ing ma ke e iciency han he dissemina ion one. In he
dissemina ion case inside s’ ansac ions elease unambi guous signals abou he alue
o he asse , a leas w hen h e p esence o inside s is com mon knowledge. Con e sely,
in h e agg ega ion case he p oce ss o e ie ing in o ma ion is by cons uc ion subjec
o e o s. Consequen ly, making i n e ence on he ue s a e o he wo ld is mo e
p ob lema i c in he la e case. Comp ehensi e ecen su eys on ex pe imen al inancial
ma ke s can be ound in No ussai and Tucke ( 2013), and Mo one and Nuzzo (2016).
Hayek (1945) and Mu h (1961) a gued ha ma ke s ne e ail in agg ega i ng he
a ailable i n o ma ion. In a pionee ing wo k, Plo and Sunde (1988) s udied
in o ma ion agg ega ion in h ee di e en ly designed ma ke s and showed ha his is
no gene ally he case. In pa icula , while he p ice mechanism e icien ly agg ega ed
he dispe sed in o ma ion bo h in ma ke s whe e pa icipan s aded a comple e se o
A o w-Deb eu secu i ies and in ma ke s whe e ade s had iden ical payo s uc u es,
agg ega ion ailed in single secu i y ma ke s whe e ade s we e paid di e en
di i dends upon he ealiza ion o unce ain y. T he au ho s explain ed his esul a guing
ha ade s canno in e he con ingen s a e o he ma ke om o he agen s’ ading
beha io when hei payo s uc u es di e . Fo sy he and Lundholm (1990) ound ha ,
in spi e o he e ogeneous di idend s uc u es in incomple e ma ke s, in o ma ion was
co ec ly agg ega ed whene e he di idend dis ibu ion was common knowledge
among ade s and he su bjec s had p e iously expe ienced he ad ing ins i u ion.
O he s ud ies ound e en mo e nega i e esul s on he c apaci y o ma ke s o
agg ega e in o ma ion unde mo e gene al condi ions han he ones c onside ed in
p e ious s udies. O'B ien and S i as a a (1991) s howed ha , e en wi h uni o m an d
common di idend dis ibu ions, ma ke s did no manage o agg ega e he dispe sed
in o ma ion i some elemen s o complexi y (mul i-pe iod asse s, no common
knowledge abou in o ma ion dis ibu ion) a e in oduced in he ma ke design. Noe h
e al. (1999) ound ha in o ma ion agg ega ion migh be hinde ed by he exis ence o
“in o ma ion aps”. In pa icula , misal igned pa e ns, in which ac ions a e based on
w ong belie s a bou o he s’ in o ma i e se , can esul in in o ma ion no being
co ec ly e ealed in o p ices. B andouy e al. (2000) p o ided u he e idence a bou
p ice o ma ion, asymme ic in o ma ion and ade s’ beha iou , in he con ex o
asymme ic and possibly misleadi ng in o ma ion in a (double-auc ion) s ock ma ke .
7
They ound ha asymme ic in o ma ion eleased i s e ec in o he ma ke only when
i is common knowledge among ma ke pa icipan s. Plo e al. (2003) ound ha
in o ma ion agg ega ion s ic ly de pends on he en i onmen complexi y. Wh ile he
compe i i e equilib ium ( a ional expec a ions model) is e y likely o hold in simple
con ex s, p i a e in o ma ion based models a e gene ally mo e accu a e in mo e
complica ed en i onmen s. In a ma ke whe e in o ma ion abou he in insic alue o
an asse is cumu la i ely dis ibu ed among ade s, Hube e al. (2008) p o ed he
exi s ence o a wide ange o le els o in o ma ion o which acqui ing addi ional
in o ma ion di d no p oduce hi ghe gains. A posi i e ela ion sh ip be ween in o ma ion
and highe p o i s was de ec ed only o e y high in o ma ion le els.
Among he s udies ha analyzed he impac o inside in o ma ion, Scho e and
Yo ulmaze (2009) ound ha eleasing in o ma ion o some inside s helped o
dec ease he a e o bank un s in an expe imen o e banking c isis. A s we shall see, we
ob ain a simila esul in he con ex o inancial ma ke s, as h e p esence o inside s
aises e iciency (see sec ion 4).
Simila ly o he s udies dealing wi h in o ma i on agg ega ion, in ou expe imen al
ma ke s all agen s a e only impe ec ly in o med on he undamen al alue o he asse .
No ade is gi en enough in o ma ion o know wi h ce ain y he u u e alue o he
asse . No ne heless, we in oduce wo majo no el ies. Fi s , in wo o ou expe imen al
condi ions “quasi-i nside s” ecei e a la ge numbe o signals han o h e s. Al hough we
can no , s ic ly speaking, alk abou a p ocess o dissemina ion o in o ma ion, we a e
none heless in e es ed in s udying he impac on ma ke e iciency o cen alizing
in o ma ion in he hands o ew agen s.
Second, di e en ly om all p e ious s udies, in ou design ade s a e gi en he
chance o sha e hei in o ma ion se wi h he o he membe s o hei g oup be o e
ading begins. We expec ha us and ecip oci y may p o e ele an mo i a ions as
ound in he li e a u e s udying s anda d coope a ion p oblems (Feh and Fischbache ,
2002). In ac , g ou p a achmen and social iden i y may also play a ole (B ewe , 2008).
The p esence o quasi-inside may ei h e induce a s onge sense o iden i y in g oups
o non-quasi-in side s, o a heigh ened pe cep ion o he un ai ness o he p ocess (Feh
and Schmid , 1999; T au ma nn, 2009; K awczyk, 2011). In bo h cases we would expec
g oups o less-in o med ade s o inc ease coope a ion in compa ison wi h symme ic
ea men s. This would lead o smoo hing he in o ma ion dis ibu ion he e ogenei y
8
and o inc easing he low o in o ma ion among ade s
3
. To he bes o ou k nowledge,
ou pape is he i s s udying in o ma ion agg ega ion in a amewo k whe e
coope a ion, ecip oci y and leade ship all ma e o agen s’ choices and p ice
dynamics.
3 Expe imen al Design
3.1 Gene al Design
We un 27 independen expe imen al ma ke s whe e a o al o 324 agen s aded a
gene ic inancial asse . Each age n was p o ided wi h 1000 okens and en uni s o
asse . Each oken was wo h 0,02 Eu os. A he end o he ading pe iod, he asse paid
an unce ain di idend D, wh ich c ould be wo h en okens o ze o okens, depending
on wo equally likely s a es o he wo ld. A he beginning o he pe iod, agen s ecei ed
pa ially in o ma i e signal(s) on he undamen al alue o he secu i y. Be o e ading
s a ed, in wha we call he sha ing s age, each ade independen ly decided whe he
o no o e eal he signal(s) o he o he wo membe s o he g oup o no .
We designed ou ea men s in addi ion o a baseline condi ion w he e no agen
ecei ed any in o ma ion. In ea men 1 (T 1) all agen s ecei ed one signal; in
ea men 2 (T2) basic-in o med agen s ecei ed one signal and quasi-i nside agen s
ecei ed h ee signals; in ea men 3 (T3) all agen s ecei ed h ee signals; in
ea men 4 (T4) basic-in o med agen s ecei ed one signal and quasi-inside agen s
ecei ed nine signals. Th ee ma ke s we e un o he baseline condi ion, while six
ma ke s we e un o each o he ou ea men s.
This design allows us o conside se e al in a ian s o ea men s compa ison.
T1 and T2 di e because o he p esence o qua si-inside s bu p ese e he amoun o
in o ma ion gi en o basic- in o med agen s. T3 and T4 di e because o he p esence
o quasi-inside s agen s bu p ese e he o al amoun o in o ma ion in he ma ke . T1
and T3 do no include quasi-inside s agen s b u di e in he amoun o in o ma ion
gi en o basic-in o med agen s. T2 and T4 bo h include quasi-inside s bu di e in he
amoun o addi ional in o ma ion gi en o hem.
3
In a companion pape , we s udy in de ail how sensi i e he p e- ade coope a ion mechanism is o he
p esence o quasi-in side s.
9
Each ma ke included 23 ading pe iods, h e e o which we e ial pe iods while
all o he 20 ensuing pe iods we e paid o . The expe imen was p og ammed in z-T ee
(Fischbache , 2007) and was un a he Labo a o y o Expe imen al Economics (LEE)
o Uni e si a Jaume I (Cas ello n, Spain). Ins uc ions a e epo ed in he App endix G.
3.2 S a e o in o ma ion
In all cases excep he baselin e, ade s ecei ed pa ially in o ma i e signal(s) on he
u u e alue o he asse di idend be o e ading s a ed. Signals we e no 100%
eliable. Assuming ha he ue di idend o be paid a he end o he pe iod was en
(ze o), he p obabi li y o ge ing a signal indica ing ha he di idend would be en
(ze o) was p. (1 – p) was he e o e he p obabili y o ge ing a p i a e signal indica ing
ha he di idend would b e en ( ze o) while he ue alue o he di idend was ins ead
ze o ( en). In o he wo ds, p was he p obabili y ha he signal e eals he ue alue
o he di idend, while 1-p is he c omplemen a y p obabili y ha he signal indica ed a
w ong alue o he di idend. We se p e qual o 70%. The alue o p was common
knowledge among subjec s.
A he beginning o he expe imen al session, in ea ch ma ke 12 ade s we e
andomly assigned o ou di e en g ou ps, each composed by h ee ade s. The g oup
composi ion was ixed h oughou he session. Be o e ading began, subjec s wen
h ough a sha ing s age, in which hey simul aneously decided whe he o no o sha e
hei signal(s) wi h o he s in hei g oup. In o ma ion sha ing could only occu wi h
componen s o he same g oup. Mo eo e , i one ade decided o sha e he
in o ma ion, all his o he signal(s) would be sha ed wi hin he g oup. No dec ep ion
when sha ing signals was allowed.
T ea men
T1
T2
T3
T4
Baseline
Panel A
Ex-An e
Numbe o signals
dis ibu ed o
“basic in o med”
ade s
1
1
3
1
-
Numbe o signals
dis ibu ed o
“quasi inside ”
ade s
-
3
-
9
-
16
Al e na i e Hypo hesis 1(a): Keeping cons an he o al numbe o signals,
p ices exhibi a signi ican close con e gence o he e icien p ice when in o ma ion
is uni o mly dis ibu ed.
Al e na i e Hypo hesis 1(b): Keeping cons an he o al numbe o signals,
p ices exhibi a signi ican close con e gence o he e icien p ice when quasi-inside
agen s a e p esen in he ma ke , i.e. when in o ma ion is cen alized.
As a second s ep, conside ing hose cases in which quasi-inside agen s a e
p esen in he ma ke (T2 and T4), we es whe he an inc ease in he numbe o quasi-
inside s’ pe capi a signals imp o es he con e gence owa d he e icien p i ce. Indeed,
in T2 and T4, while basic in o me d agen s we e p o ided wi h one signal each, quasi-
inside agen s ( h ee subjec s who belong o he same g oup) we e gi en h ee an d nine
signals each espec i ely. The e o e, we o mula e hypo hesis 2 and i s al e na i es.
Hypo hesis 2: O he hings being equal, when quasi-inside agen s a e p o ided
wi h h ee signals each, p ices exhibi he same de ia ion om he e icien p ice as
when quasi-inside agen s a e p o ided wi h nine signals each.
Al e na i e Hypo hesis 2(a): O he hings being equal, when quasi-inside
agen s a e p o ided wi h h ee signals each, p ices exhibi a signi ican close
con e gence o he e icien p ice han when hey a e p o ided wi h nine signals
each.
Al e na i e Hypo hesis 2(b): O he hings being equal, when quasi-inside
agen s a e p o ided wi h nine signals each, p ices exhibi a signi ican close
con e gence o he e icien p ice han when hey a e p o ided wi h h ee signals
each.
Finally, conside ing he cases whe e in o ma ion is uni o mly dis ibu ed among
ade s (T1 and T3), we es whe he inc easing he numbe o signals in he ma ke
impac s on ma ke e iciency. This can be es ed because each agen is p o ided wi h
one and h ee signal(s) in T1 and T3, espec i ely. Ou hi d hypo hesis and i s
al e na i es a e s a ed below:
Hypo hesis 3: When in o ma ion is uni o mly dis ibu ed and ade s a e
p o ided wi h one signal each, p ices exhibi he same de ia ion om he e icien
p ice as when ade s a e p o ided wi h h ee signals each.

17
Al e na i e Hypo hesis 3(a): When in o ma ion is uni o mly dis ibu ed,
p ices exhibi a signi ican close con e gence o he e icien p ice when ade s a e
p o ided wi h one signal each.
Al e na i e Hypo hesis 3(b): When in o ma ion is uni o mly dis ibu ed,
p ices exhibi a signi ican close con e gence o he e icien p ice when ade s a e
p o ided wi h h ee signals each.
5 Resul s
5.1 In o ma ion sha ing
We i s analyze how ade s use he op ion o sha e hei p i a e in o ma ion; secondly
we p esen esul s on ma ke ou comes.
Figu es 1 and 2 illus a e how subjec s use he coope a ion mechanism. They
epo he a e age numbe o signals s ha ed in each o he six ma ke s comp ising a
gi en ea men o basic in o med agen s’ (Figu e 1) and quasi-inside agen s (Figu e
2).
Figu e 1: In o ma ion sha ing by basic-in o med
agen s
Figu e 2: In o sha ing by quasi -inside s agen s
We i s compa e in o ma ion s ha ing pa e ns in T1 and T3, whe e no quasi-
inside agen is p esen . Th oughou ou desc ip i e analysis, we conside each ma ke as
yielding one independen obse a ion. Indeed, since he same g oup o people wi hin a ma ke
in e ac o e se e al pe iods, wi hin-g oup obse a ions a e se ially in e dependen . This
p ope y makes i sui able o conside each g oup (ma ke ) as an independen obse a ion, e.g.
0.2 .4 .6 .8 1
1 2 3 4
T ea men
In o Sha ing (%) Median Line
Only basic in o med agen s included
In o ma ion sha ing o e ea men s
0.2 .4 .6 .8 1
42 T ea men
In o Sha ing (%) Median Line
Only quasi inside s included
In o ma ion sha ing o e ea men s
18
by compu ing he mean (m edian) o he a iable o in e es o e he pe iods comp ising a gi en
ma ke (see F e che e, 2012). We no e ha ade s coope a e signi ican ly less in T 3 ( wo-
ailed k-sample median es : N = 6; Pea son chi squa e = 5.33; P = 0.021. See also Table
A1, Appendix A). This is likely he conseq uence o ade s’ ini ial in o ma ion se being
la ge in T3 compa ed o T1. Agen s can hus be mo e con iden in T3 han T1 ha hei
in o ma ion s e is su icien o i ndica e he ue s a e o h e wo ld. In o he wo ds, he
expec ed bene i s om coope a ion is lowe in T3 han T1, hence he incen i es o
sha e in o ma ion a e also lowe .
We a lso ind ha he le el o in o ma ion sha ing among basic in o med age n s
does no signi ican ly change when quasi- insi de agen s a e in oduced in he m a ke ,
as can be seen in he com pa ison be ween T1 - agen s p o ided wi h one signal each - and
T2 - basic in o med and quasi-inside agen s p o ided wi h one and h ee signals each,
espec i ely - ( wo- ailed k-sample median es : N = 6; Pea son chi squa e = 0.00; P = 1.000.
See also Table A2, Appendix A) and be ween T1 and T4 - basic in o med and quasi-inside
agen s p o ided wi h one and nine signals each espec i ely – ( wo- ailed k-sample median
es : N = 6; Pea son chi squa e = 0.00; P = 1.000. See also Table A3, Appendix A).
Fu he mo e, mo ing om T2 o T4, he median pe cen age o basic in o med ade s
sha ing hei in o ma ion se swi ches om 57.22% o 63.61%. Ye , his di e ence is
no s a is ically signi ican ( wo- ailed k-sample median es : N = 6; Pea son chi squa e =
0.00; P = 1.000. See also Table A4, Appendix A). Finally, no signi ican di e ence ( wo-
ailed k-sample median es : N = 6; Pea son chi squa e = 1.33; P = 0.248. See also Table A5,
Appendix A) eme ges be ween quasi-insid e s’ in o ma ion sha i ng beha io in T2 and
T4, al hough i is appa en om Figu e 2 ha sha ing is lowe in T4 ha n T2. This
beha io p esumably ollows he same easons as he d op in sha ing o basic
in o med agen s in T3 ela i e o T1. Tha is, a highe numbe o ini ial signals o each
agen educes hei need o coope a e wi h o he s. Ou conjec u e (s ee sec ion 2) ha
p ocedu al un ai ness in he asymme ic ea men s may ha e led o s onge “g oup
spi i ” in basic-in o med agen s is hus discon i med by he da a. As ound in a
companion pape , hough, some o he iden i y e ec s, which a e no ele an o he
p esen pape , seem none heless o eme ge.
5.2 Ma ke E iciency
5.2.1 Gene al O e iew
19
Figu es 5-8 epo he box-plo s o he RMSE dis ibu ion o e ach o he benchma k
p ices in each ea men . These g aphs pool RMSE o e pe iods and ma ke s. A mo e
de ai led o e iew can be ound in Figu es B1, B2, B3, B4, and B5 in Appendix B . The e
we show he ac ual e olu ion o he aded p ices in ela ion o he benchma k p ices,
b oken down by ma ke and pe iod.
Fi s , we no e a clea di e ence be ween he baseline condi ion and all o he
ea men s. The unin o med and di idend p ice RMSE dis ibu ions a e shi ed
downwa d and upwa d, espec i ely, in compa ison o all o he ea men s. Th ough
he use o a Tobi eg ession analysis (see Appendix C, Model C1), we ind ha he
unin o med p ice RMSE in he baseline is signi ican ly lowe han ha compu ed in
each o he o he ea men s (P < 0.00 1 in all he ou pai wise compa isons). On he
con a y, we ind ha he di idend p ice RMSE dis i bu ion in he baseline condi ion is
signi ican ly highe wi h espec o ha compu ed in each o he o he ea men s (P <
0.05 in all he ou pai wise compa isons). This p elimina y analy sis shows ha when
no in o ma ion is p esen in he ma ke , ade p ices emain signi ican ly close o he
unin o med p ice and u he away om he di idend p ice han when some
in o ma ion is p esen in he ma ke . In pa icula , we no e h a his di e ence is mo e
p onounced o he unin o med p ice han he di idend p ice. I is ela i ely easie o
ma ke s wi h in o ma ion o depa away om he unin o med p ice han o come
close o he undamen al in compa ison o ma ke s wi hou in o ma ion. In ac , ade
p ices in he baseline condi ion exhibi a andom walk p ocess a ound he expec ed
alu e o he di idend dis ibu ion, and in n o case p ices each he di idend alue (see
Figu e B 5, Appen dix B). We e mploy a Tobi eg ession model (see Appendix C, Model
C2) o assess whe he , when no in o ma ion is in he ma ke , he dis ance be ween
ade p ices and he unin o med p ice i s lowe han he dis ance be ween ade p ices
and he undamen al alue o he asse . This i s he s anda d assump ion in ma ke s
wi h no in o ma ion, and i is, no su p isingly, con i med in ou case (coe . = -4.18; P
< 0.001). This p elimina y e idence e nsu es ha agen s we e able o exploi he
a ailable in o ma ion and aded a p ices ha we e u he away om he unin o med
p ice and close o he undamen al asse alue han in he baseline.
20
Figu e 5: RMSE Dis ibu ion, Unin o med P ice
Figu e 6: RMSE Dis ibu ion, Bayes P ice
Figu e 7: RMSE Dis ibu ion, E icien P ice
Figu e 8: RMSE Dis ibu ion, Di idend
Among he ea men s wi h in o ma ion, we no e some endency o he
uni o med p ice RMSE o inc ease as we mo e om T1 o T4, and co espondingly
( hough less ma kedly so) o he di idend p ice RMSE o dec ease as we mo e om T1
o T4. This may signal ha he combina ion o adding in o ma i on and cen alizing
in o ma ion helps agen s o ade a p ic es ha a e close o he unda men al.
Ne e heless, we no e no clea pa e n wi h espec o ei he he Bayes RMSE o he
Fama-e icien p ice.
We conjec u e ha his appa en lack o ea men di e ences in he Bayes and
Fama-e icien RMSE may be due o lea ning e ec s. Lea ni ng may occu because
agen s upda e hei decisi on-making ules as hey accumula e ading expe ience.
Agen s c an imp o e hei abili y o in e in o ma ion om he o he ade s’ ac i i y
o e he cou se o 20 pe iods. Agen s may also upda e hei coope a ion s a egies o e
ime, hus also a ec ing h e way ma ke s sp ead i n o ma ion. In ac , ime se ies plo s
in Appen dix B ypically exhibi p oximi y o unin o med o Bayesian p ice s in ea ly
pe iods, and p oximi y o he Fama-e icien p ice in he la e pe iods o he session. Fo
ins ance, in ma ke 1 om ses sion 2 and T2 (see appendix B, Figu e B2), unin o med
ades domina e he i s h ee pe iods, p ices hen con e ge o he Bayes p ice in
012345
RMSE Unin o med P ice
Baseline T ea men 1
T ea men 2 T ea men 3
T ea men 4
02468
RMSE Bayes P ice
T ea men 1 T ea men 2
T ea men 3 T ea men 4
02468
RMSE E icien P ice
T ea men 1 T ea men 2
T ea men 3 T ea men 4
0246810
RMSE Di idend P ice
Baseline T ea men 1
T ea men 2 T ea men 3
T ea men 4
21
pe iods om ou o nine, and p ices ack he e icien eq ui lib ium p ice o all la e
pe iods. This sugges s a pa e n whe eby agen s ade as i hey we e unin o med in
he ea lies pe iods, p ocess hei own p i a e in o ma ion in in e media e pe iods, and
e en ually man age o co ec ly pool he in o ma ion dispe sed in he ma ke in he inal
pe iods. Lea ning may hus be ele an no only o accoun o indi idual beha io bu
also o i s impac on ma ke pe o mance.
Fo hese easons, we spli ou desc ip i e esul s in o he i s and second block
o en pe iods in each ma ke
5
and epo on he benchma ks pe o man ce a es o e
he ou ea men s. We iden i y o each p e iod o each ma ke which benchma k p ice
is bes able o app oxima e he ac ual an sac ion p ices. Mo e p ecis ely, we selec he
benchma k p ice wi h he lowes RMSE alue om ac ual p ices
6
. Essen ially, in each
ea men we coun how many imes a gi en benchma k bes app oxima es ou da a.
Table 2 epo s he pe cen ages o each b enchma k being selec ed as he one wi h he
lowes RMSE.
Pe o mance Ra es
Unin o med P ice
Bayes P ice
E icien P ice
Di idend
T ea . 1 Fi s Hal
45.00%
45.00%
10.00%
0.00%
T ea . 1 Second Hal
45.00%
38.33%
16.67%
0.00%
T ea . 2 Fi s Hal
43.33%
46.67%
10.00%
0.00%
T ea . 2 Second Hal
21.67%
28.33%
50.00%
0.00%
T ea . 3 Fi s Hal
50.00%
50.00%
0.00%
0.00%
T ea . 3 Second Hal
35.00%
46.67%
18.33%
0.00%
T ea . 4 Fi s Hal
43.33%
48.33%
8.33%
0.00%
T ea . 4 Second Hal
15.00%
38.33%
46.67%
0.00%
Baseline Fi s Hal
100.00%
/
/
0.00%
Baseline Second Hal
100.00%
/
/
0.00%
5
Box-Plo s a e epo ed in Appendix D.
6
In case o ies be ween RMSE o wo o mo e benchma ks, we selec he leas e icien benchma k. This
is on he o ne hand he mos conse a i e c i e ion o ou analysis and on he o he hand pe mi s
pe o mance a es o always sum up o 100%.

22
Table 2: Benchma k pe o mance a es, g oup ed by ea men and i s o second blo ck o en pe iods.
Fi s , we no e ha he Di idend p i ce has ne e he lowes RMSE, deno ing he
di icul y o ade s o achie ing he undamen al p ice. Wi h ega ds o he h ee o he
benchm a k s, in T1 he unin o med and he Bayes p ices a e he bes pe o ming
benchma ks in bo h he i s and he second 10 - block pe iods, wi h a pe o mance a e
o 45% and 45%, espec i ely, in he i s 10-block pe i od, and o 45% and 38.33% in
he second 10-block pe iod. The e icien p ic e ma ginally i mp o es om a
pe o mance a e o 10% in he ea ly pe iods o a pe o mance a e o 16.67% in la e
pe iods. T ading in T1 is hus s ill p edominan ly unin o med o based on p i a e
in o ma ion.
In T2 he unin o med and he Bayes p ices a e he b es pe o ming ones in ea ly
pe iods (wi h a pe o mance a e o 43.33% and 46.67% espec i ely). Ne e heles s,
when we mo e o la e pe iods he e icien p ice becomes he b es acked benchma k
(wi h a pe o mance a e o 50%). I is pa icula ly in e es ing o no e how unin o med
ades dec ease om 43.33% o 21.67% and e icien ades inc ease om 10% o 50%
when mo ing om ea ly o la e pe iods. This e idence shows ha , o e ime, ade s
imp o e h ei abili y o in e and agg ega e he in o ma ion dis pe sed in he ma k e .
In T3 esul s a e ema kably simila o T1. Bo h he unin o med and he Bayes
p ices pe o m be e in accoun ing o ou da a han he e icien p ice in bo h ea ly
and la e pe iods. I n pa icula , in he second en- ound block, he Bayes p ice is he bes
ac ked bench ma k wi h a pe o mance a e o 46.67%. I is ema kable ha , in spi e
o he numbe o ini ial signals being ex an e h ee imes as high in T3, we obse e
ma ke p ices o ha e he same le els o p oximi y o he e icien p ice and he B ayes
p ice as in T1. This is no due o he ac ha he ex pos numbe o signals is si mila in
he wo ea men s. As Table 1, Panel B, shows, agen s in T3 ha e a signi ican ly (Mann
Whi ney U es : N
7
= 6; z = -2.882; P < 0.0039) la ge amoun o in o ma ion (5 .90 signals
pe capi a) han in T1 (2.18 signals pe capi a). The ex pos a io o numbe o signals
is 2.70, which is less han he ex an e a io o 3:1 bec ause agen s sha ed on a e age less
in T3 han T1. The bad pe o mance o he e icien p ice sugges s ha ade s a e
mainly conce ned wi h p ocessi ng hei own p i a e in o ma ion han yi ng o in e
o he s’ in o ma ion h ough he obse a ion o p ice signals.
7
Ma ke a e ages o he ex-pos signals dis ibu ion a e used o accoun o wi hin ma ke co ela ion.
23
Finally, benchma ks in T4 pe o m simila ly o T2. While he unin o med and he
Bayes p ices exhibi he highes pe o man ce a es in ea ly pe iods (43.33% and
48.33% espec i ely), he e icien p ice pe o ms be e in la e pe iods (wi h a
pe o mance a e o 46.67%). E en in his case i is ema kable how he e icien p ice
pe o mance a e swi ches om 8.33% o 46.67% mo ing om ea ly o la e pe iods.
He e again we no e ha in spi e o a la ge numbe o signals being a ailab le in T4
compa ed o T 2 bo h ex an e - in a p opo ion o 2:1 - han ex pos - in a p opo ion o
1.9:1 (Mann Whi ney U es : N
8
= 6; z = -2.892; P < 0.0038) – he pe o mance in e ms
o e iciency appea o be i ually he same.
5.2.3 Econome ic Analysis
In his sec ion we pe o m a ho ough ec onome ic analysis o ou hy po heses and o
he conjec u es ha eme ged om he desc ip i e analysis. Fo his pu pose we use he
ollowing Tobi eg ession model:
𝑅𝑀𝑆𝐸𝑖,𝑡 =𝛼+∑𝛽𝑖
𝑛
𝑖=1 ∙𝑀𝑘𝑡𝑖+𝛾∙𝑃𝑒𝑟𝑖𝑜𝑑+∑𝜃𝑗
𝑘
𝑗=1 ∙𝑋𝑖,𝑗+𝜀𝑖,𝑡
The RMSE index o ac ual ade p ices wi h espec o a gi en p ice benchma k is he
dependen a iable o he model. Ou co a ia es include a dummy a iable 𝑀𝑘𝑡𝑖 o
each o n ma ke s bu one ha is omi ed. In his way we con ol o bo h possi ble
hydiosinc acies ac oss ma ke s and o he clus e ing o ou da a a he ma ke le el.
𝑃𝑒𝑟𝑖𝑜𝑑 is a end a iable cap u ing he ime e ec ; and 𝑋
𝑖,𝑗 is a ec o o d emog aphics
and a i udinal a iables
9
ha a e a e aged a he ma ke le el.
We es o ea men e ec s pe o ming Wald es s o e he di e e nce be ween he
sums o ma ke dummy coe icien s belonging o di e en ea men s. Tha is, o es
o he null hypo hesis o absence o di e ences be ween wo ea men s, we conside
he null hypo hesis:
8
Ma ke a e ages o he ex-pos signals dis ibu ion a e used o accoun o wi hin ma ke co ela ion.
9
A de ailed d esc ip ion o he demog aphics and a i udinal a iables is epo ed in he no e below Table
E1 (Appendix E).
24
𝐻0: 𝑍𝑟,𝑠 ≡∑βi,
𝑛𝑟
i=1 −∑βi,s
𝑛𝑠
i=1 =0
whe e and s iden i y he ma k e s associa ed wi h wo di e en ea men s. 𝑛𝑟 and 𝑛𝑠
a e he numbe s o ma ke s belonging o ea men and s. Ou design includes six
ma ke s o each ea men . 𝑛𝑟 and 𝑛𝑠 a e he e o e always equal o six, excep o he
ea men o which he omi ed ca ego y o he model belongs (T ea men 1). No e ha
he possibili y ha 𝑛𝑟>𝑛𝑠 o compa isons in ol ing T ea men 1 does no a ec he
es ima ion o ou pai wise c ompa isons, since he omi ed ca e go y coe icien is
implici ly ze o.
Since ou desc ip i e analysis highligh ed he p esence o di e en p i ce pa e ns
be ween he i s and second hal ma ke pe iods, we un he econome ic model bo h
in he i s and he sec ond block o en pe iods as well as o e he en i e se o ma ke
pe iods.
All he eg ession ou pu s a e epo ed in Appendix E; all he ea men s pai wise
compa isons a e a ailable in Appendi x F.
He e we mainly oc us on he esul s de i ed om he s econd block o en pe iods.
Resul 1: Hypo hesis 1 is ejec ed. We ind ha , keeping in o ma ion cons an ex
an e (36 signals in he ma ke ), when quasi-inside agen s a e ac i e in he ma ke (T4),
ac ual p ices exhib i a signi ican ly close con e gence o he e icien p ice wi h
espec o he case in which in o ma ion is uni o mly dis ibu ed (T3) (𝑍𝑇4,𝑇3 = -4.40; P
= 0.014). The e o e , keeping cons an he quan i y o in o ma ion in he ma ke , a
cen alized in o ma ion dis ibu ion in which some agen s a e p o id ed wi h mo e
in o ma ion gua an ees mo e e iciency han a uni o m in o ma ion dis ibu ion in
which all subjec s ecei e he same amoun o in o ma ion.
Resul 2: We canno ejec Hypo hesis 2. We ind ha , o he hings being equal,
when quasi-inside ade s a e gi en nine signals (T4), ma ke e iciency is no
signi ican ly highe han when quasi-inside agen s a e p o ided wi h h ee signals
each (T2) (𝑍𝑇4,𝑇2 = -0 .79; P = 0.710). I n o he wo ds, when i n o ma ion is pola ized,
p o iding quasi-inside agen s wi h a g ea e numbe o pe -capi a signals does no
signi ican ly inc ease ma ke e iciency.
Resul 3: We canno ejec Hypo hesis 3. When in o ma ion is uni o mly
dis ibu ed, swi chi ng om a ma ke whe e subjec s a e p o ided wi h one signal each
25
(T1) o a ma ke whe e h ee signals a e eleased o each subjec (T3) does no lead o
a signi ican inc ease in he ma ke e iciency le el (𝑍𝑇3,𝑇1 = -1.58; P = 0.384). We
conjec u e ha he common knowledge ha in o ma ion is uni o mly dis ibu ed leads
subjec s no o ecognize he p esence o an in o med ma ke leade and, as a
consequen ce, no o ocus on he o he s’ ading ac i i y. In ac , he sign o he
coe icien indica es ha he con e gence o he e icien p ice is highe in T1 han in
T3. This is ema kabl e, as he numbe o ini ial signals is h ee imes highe in T3 han
in T1 (keeping ixed he uni o m dis ibu ion in bo h ea men s). We conjec u e ha
he g ea e amoun o in o ma ion in T3 makes ade s mo e con iden in being able o
co ec ly o ecas he asse di idend and makes hem less p one o use he ma ke
ading ac i i y as an in e ence ool. On he con a y, when p o ided wi h only one
in o ma i e signal (as in T1), ade s ocus mo e on he ma ke ac i i y o imp o e hei
chance o p ope ly in e ing he asse undamen al alue and, consequen ly, ma ke
e iciency is imp o ed.
Wi h ega d o he e maining be nchma ks, we ind ha addi ional in o ma ion is
no disca ded bu is somehow p ocesse d by ade s. This is e iden om he inc eas ing
pa e n o e ea men s o he unin o med p ice RMSE in la e pe i ods. In o he wo ds,
mo ing om T1 o T4, as he quan i y o in o ma ion ( o al numbe o signals)
inc eases, p ices de pa om he unin o med p ice. This end is in place in all he
pai wise compa isons (𝑍𝑇1,𝑇2 = -4.93; P = 0.00; 𝑍𝑇1,𝑇3 = -3.89; P = 0.000; 𝑍𝑇1,𝑇4 = - 8.29;
P = 0.000; 𝑍𝑇2,𝑇4 = -3 .80; P = 0.0 01; see Table F8, Appen dix F) bu on e (𝑍𝑇2,𝑇3 = 0.40; P
= 0.717; see Table F8, Appendix F). In e es ingly, e en i no signi ican , he sign o he
Wald es 𝑍𝑇2,𝑇3 appea s o con adic he ule “mo e in o ma ion less noise ”. Indeed,
al hough in T3 ade s ecei e wice as many signals as i n T2, p ices come close o he
unin o med p ice when only basic-in o med agen s a e ac i e in he ma ke (T3)
10
.
Cohe en ly wi h ou esul s on he e icien p ice, we also ind ha e en k eeping
iden ical he amoun o in o ma ion wi hin he ma ke (i.e. in T3 and T4), asymme ic
in o ma ion dis ibu ions p oduce lowe noise ha n h e case in which in o ma ion is
ins ead symme ically sp ead ou (𝑍𝑇3,𝑇4 = -4.21; P = 0.000; see Tab le F8, Appendix F).
10
In e es ingly, when in o ma ion is ins ead asymme ically dis ibu ed, doubling he o e all amoun o
signals leads p ices away om he unin o med p ice (𝑍𝑇2,𝑇4 = -3.80; P = 0.001)
32
APPENDIX A
T1
T3
To al
Obse a ions
Lowe han he
median
1
5
6
G ea e han he
median
5
1
6
To al
6
6
12
Pea son chi-squa e (1) = 5.3333 P = 0.021
Table A1: Median es on in o ma ion sha ing
( eamen s 1 and 3)
T1
T2
To al
Obse a ions
Lowe han he
median
3
3
6
G ea e han he
median
3
3
6
To al
6
6
12
Pea son chi-squa e (1) = 0.0000 P = 1.000
Table A2: Median es on in o ma ion sha ing ( ea -
men s 1 and 2), only basic-in o med included
T1
T4
To al
Obse a ions
Lowe han he
median
3
3
6
G ea e han he
median
3
3
6
To al
6
6
12
Pea son chi-squa e (1) = 0.0000 P = 1.000
Table A3: Median es on in o ma ion sha ing ( ea -
men s 1 and 4), only basic-in o med included
T2
T4
To al
Obse a ions
Lowe han he
median
3
3
6
G ea e han he
median
3
3
6
To al
6
6
12
Pea son chi-squa e (1) = 0.0000 P = 1.000
Table A4: Median es on in o ma ion sha ing ( ea -
men s 2 and 4), only basic-in o med agen s included
T2
T4
To al
Obse a ions
Lowe han he
median
2
4
6
G ea e han he
median
4
2
6
To al
6
6
12
Pea son chi-squa e (1) = 1.3333 P = 0.248
Table A5: Median es on in o ma ion sha ing ( ea -
men s 2 and 4), only quasi-inside s agen s included

33
APPENDIX B
0246810
0120 240 360 480 600 720 840 960 1080 1200 1320 1440 1560 1680 1800 1920 2040 2160 2280 2400
Time
P ice Di idend
Unin o med P ice Bayes P ice
E icien P ice
T1-S1-M1
0246810
0120 240 360 480 600 720 840 960 1080 1200 1320 1440 1560 1680 1800 1920 2040 2160 2280 2400
Time
P ice Di idend
Unin o med P ice Bayes P ice
E icien P ice
T1-S3-M1
0246810
0120 240 360 480 600 720 840 960 1080 1200 1320 1440 1560 1680 1800 1920 2040 2160 2280 2400
Time
P ice Di idend
Unin o med P ice Bayes P ice
E icien P ice
T1-S3-M2
34
Figu e B1: T ade p i ces in T ea men 1
0246810
0120 240 360 480 600 720 840 960 1080 1200 1320 1440 1560 1680 1800 1920 2040 2160 2280 2400
Time
P ice Di idend
Unin o med P ice Bayes P ice
E icien P ice
T1-S3-M3
0246810
0120 240 360 480 600 720 840 960 1080 1200 1320 1440 1560 1680 1800 1920 2040 2160 2280 2400
Time
P ice Di idend
Unin o med P ice Bayes P ice
E icien P ice
T1-S10-M1
0246810
0120 240 360 480 600 720 840 960 1080 1200 1320 1440 1560 1680 1800 1920 2040 2160 2280 2400
Time
P ice Di idend
Unin o med P ice Bayes P ice
E icien P ice
T1-S10-M2
35
0246810
0120 240 360 480 600 720 840 960 1080 1200 1320 1440 1560 1680 1800 1920 2040 2160 2280 2400
Time
P ice Di idend
Unin o med P ice Bayes P ice
E icien P ice
T2-S2-M1
0246810
0120 240 360 480 600 720 840 960 1080 1200 1320 1440 1560 1680 1800 1920 2040 2160 2280 2400
Time
P ice Di idend
Unin o med P ice Bayes P ice
E icien P ice
T2-S4-M1
0246810
0120 240 360 480 600 720 840 960 1080 1200 1320 1440 1560 1680 1800 1920 2040 2160 2280 2400
Time
P ice Di idend
Unin o med P ice Bayes P ice
E icien P ice
T2-S4-M2
36
Figu e B2: T ade p i ces in T ea men 2
0246810
0120 240 360 480 600 720 840 960 1080 1200 1320 1440 1560 1680 1800 1920 2040 2160 2280 2400
Time
P ice Di idend
Unin o med P ice Bayes P ice
E icien P ice
T2-S4-M3
0246810
0120 240 360 480 600 720 840 960 1080 1200 1320 1440 1560 1680 1800 1920 2040 2160 2280 2400
Time
P ice Di idend
Unin o med P ice Bayes P ice
E icien P ice
T2-S4-M4
0246810
0120 240 360 480 600 720 840 960 1080 1200 1320 1440 1560 1680 1800 1920 2040 2160 2280 2400
Time
P ice Di idend
Unin o med P ice Bayes P ice
E icien P ice
T2-S9-M1
37
0246810
0120 240 360 480 600 720 840 960 1080 1200 1320 1440 1560 1680 1800 1920 2040 2160 2280 2400
Time
P ice Di idend
Unin o med P ice Bayes P ice
E icien P ice
T3-S5-M1
0246810
0120 240 360 480 600 720 840 960 1080 1200 1320 1440 1560 1680 1800 1920 2040 2160 2280 2400
Time
P ice Di idend
Unin o med P ice Bayes P ice
E icien P ice
T3-S5-M2
0246810
0120 240 360 480 600 720 840 960 1080 1200 1320 1440 1560 1680 1800 1920 2040 2160 2280 2400
Time
P ice Di idend
Unin o med P ice Bayes P ice
E icien P ice
T3-S5-M3

38
Figu e B3: T ade p ices in T ea men 3
0246810
0120 240 360 480 600 720 840 960 1080 1200 1320 1440 1560 1680 1800 1920 2040 2160 2280 2400
Time
P ice Di idend
Unin omed P ice Bayes P ice
E icien P ice
T3-S8-M1
0246810
0120 240 360 480 600 720 840 960 1080 1200 1320 1440 1560 1680 1800 1920 2040 2160 2280 2400
Time
P ice Di idend
Unin omed P ice Bayes P ice
E icien P ice
T3-S8-M2
0246810
0120 240 360 480 600 720 840 960 1080 1200 1320 1440 1560 1680 1800 1920 2040 2160 2280 2400
Time
P ice Di idend
Unin omed P ice Bayes P ice
E icien P ice
T3-S8-M3
39
0246810
0120 240 360 480 600 720 840 960 1080 1200 1320 1440 1560 1680 1800 1920 2040 2160 2280 2400
Time
P ice Di idend
Unin o med P ice Bayes P ice
E icien P ice
T4-S6-M1
0246810
0120 240 360 480 600 720 840 960 1080 1200 1320 1440 1560 1680 1800 1920 2040 2160 2280 2400
Time
P ice Di idend
Unin o med P ice Bayes P ice
E icien P ice
T4-S6-M2
0246810
0120 240 360 480 600 720 840 960 1080 1200 1320 1440 1560 1680 1800 1920 2040 2160 2280 2400
Time
P ice Di idend
Unin o med P ice Bayes P ice
E icien P ice
T4-S6-M3
40
Figu e B4: T ade p i ces in T ea men 4
0246810
0120 240 360 480 600 720 840 960 1080 1200 1320 1440 1560 1680 1800 1920 2040 2160 2280 2400
A
P ice Di idend
Unin o med P ice Bayes P ice
E icien P ice
T4-S6-M4
0246810
0120 240 360 480 600 720 840 960 1080 1200 1320 1440 1560 1680 1800 1920 2040 2160 2280 2400
Time
P ice Di idend
Unin o med P ice Bayes P ice
E icien P ice
T4-S7-M1
0246810
0120 240 360 480 600 720 840 960 1080 1200 1320 1440 1560 1680 1800 1920 2040 2160 2280 2400
Time
P ice Di idend
Unin o med P ice Bayes P ice
E icien P ice
T4-S7-M2
41
Figu e B5: T ade p ices in he baseline condi ion
0246810
0120 240 360 480 600 720 840 960 1080 1200 1320 1440 1560 1680 1800 1920 2040 2160 2280 2400
Time
P ice Di idend
Unin o med P ice
Baseline-S11-M1
0.00 2.00 4.00 6.00 8.00 10.00
0120 240 360 480 600 720 840 960 1080 1200 1320 1440 1560 1680 1800 1920 2040 2160 2280 2400
Time
P ice Di idend
Unin o med
Baseline-S12-M1
0.00 2.00 4.00 6.00 8.00 10.00
0120 240 360 480 600 720 840 960 1080 1200 1320 1440 1560 1680 1800 1920 2040 2160 2280 2400
Time
P ice Di idend
Unin o med
Baseline-S12-M2
48
Table E2 con d.
T4S6M3
0.329
0.531
0.442*
(0.364)
(0.338)
(0.248)
T4S6M4
-0.681*
-0.138
-0.334
(0.400)
(0.337)
(0.253)
T4S7M1
-0.112
-0.543
-0.223
(0.613)
(0.349)
(0.361)
T4S7M2
0.421
0.240
0.439
(0.527)
(0.537)
(0.365)
age_ma ke _mean
0.0938
0.0130
0.0596
(0.0706)
(0.0615)
(0.0480)
deg_ma ke _mean
0.370
-0.856
-0.170
(0.602)
(0.627)
(0.417)
exp_ma ke _mean
-0.403**
-0.263
-0.265**
(0.200)
(0.170)
(0.126)
in_ma ke _mean
0.213
0.119
0.132
(0.276)
(0.286)
(0.194)
u _ma ke _mean
-0.313
0.0487
-0.0907
(0.252)
(0.283)
(0.187)
gende _ma ke _mean
-0.323
-0.212
-0.247
(0.318)
(0.292)
(0.227)
Cons an
1.143
3.057*
1.538
(1.897)
(1.736)
(1.301)
Obse a ions
240
240
480
Pseudo R2
0.0734
0.162
0.0826
No es: The Bayes P ice RMSE is he Dependen Va iable. See No es o Table E1 o a iables’ de ini ion.

49
Table E3: Reg ession analysis o Tobi model o p ice con e gence owa d he Unin o med
P ice
VARIABLES
Pe iods 1_10
Pe iods 11_20
Pe iods 1_20
pe iod
0.0472***
0.0526***
0.0508***
(0.0159)
(0.0193)
(0.00665)
T1S3M1
0.336
-0.832***
-0.276
(0.426)
(0.235)
(0.306)
T1S3M2
0.0687
-0.116
-0.0985
(0.265)
(0.265)
(0.207)
T1S3M3
0.836***
0.730**
0.686***
(0.274)
(0.354)
(0.228)
T1S10M1
1.173***
0.267
0.672**
(0.336)
(0.416)
(0.315)
T1S10M2
1.010**
1.698***
1.282***
(0.412)
(0.511)
(0.334)
T2S2M1
0.621**
1.582***
1.123***
(0.312)
(0.342)
(0.246)
T2S4M1
0.180
1.566***
0.846***
(0.322)
(0.381)
(0.279)
T2S4M2
0.230
1.507***
0.866***
(0.332)
(0.314)
(0.249)
T2S4M3
0.282
1.108**
0.684**
(0.307)
(0.428)
(0.279)
T2S4M4
-0.205
0.980**
0.388
(0.317)
(0.383)
(0.275)
T2S9M1
-0.0160
0.486
0.158
(0.284)
(0.323)
(0.211)
T3S5M1
0.919***
0.204
0.480*
(0.279)
(0.286)
(0.245)
T3S5M2
0.982***
0.213
0.510*
(0.352)
(0.391)
(0.298)
T3S5M3
0.755**
1.852***
1.214***
(0.298)
(0.421)
(0.277)
T3S8M1
0.196
1.574***
0.839***
(0.236)
(0.388)
(0.262)
T3S8M2
0.471**
0.842***
0.649***
(0.237)
(0.249)
(0.185)
T3S8M3
0.917***
2.138***
1.507***
(0.269)
(0.322)
(0.248)
T4S6M1
1.335***
2.092***
1.685***
(0.332)
(0.394)
(0.268)
T4S6M2
1.001***
1.882***
1.372***
(0.229)
(0.357)
(0.226)
50
Table E3 con d.
T4S6M3
1.571***
2.541***
2.058***
(0.263)
(0.228)
(0.194)
T4S6M4
0.488
2.015***
1.197***
(0.307)
(0.306)
(0.256)
T4S7M1
1.110***
1.000***
1.047***
(0.386)
(0.372)
(0.284)
T4S7M2
1.209***
1.504***
1.274***
(0.244)
(0.371)
(0.218)
age_ma ke _mean
0.00693
0.0325
0.0446
(0.0503)
(0.0598)
(0.0404)
deg_ma ke _mean
0.648**
0.950***
0.881***
(0.300)
(0.351)
(0.262)
exp_ma ke _mean
0.228**
0.182
0.171*
(0.110)
(0.142)
(0.0981)
in_ma ke _mean
0.215
0.278
0.165
(0.172)
(0.231)
(0.148)
u _ma ke _mean
0.283
0.158
0.307*
(0.177)
(0.262)
(0.163)
gende _ma ke _mean
-0.387*
-0.261
-0.202
(0.214)
(0.283)
(0.193)
Cons an
-0.397
-1.637
-1.605*
(1.167)
(1.483)
(0.940)
Obse a ions
270
270
540
Pseudo R2
0.194
0.241
0.177
No es: The Unin o med P ice RMSE is he Dependen Va iable. See No es o Table E1 o a iables’
de ini ion.
51
Table E4: Reg ession analysis o Tobi model o p ice con e gence owa d he Di idend P ice
VARIABLES
Pe iods 1_10
Pe iods 11_20
Pe iods 1_20
pe iod
-0.0691**
-0.0655*
-0.0728***
(0.0301)
(0.0357)
(0.0118)
T1S3M1
-0.00707
-0.396
-0.117
(0.777)
(0.515)
(0.478)
T1S3M2
0.434
-0.903*
-0.129
(0.549)
(0.460)
(0.362)
T1S3M3
-0.413
-1.469*
-0.893
(0.794)
(0.816)
(0.579)
T1S10M1
-0.789
-1.371*
-1.116*
(0.869)
(0.721)
(0.586)
T1S10M2
-1.510**
-2.065**
-1.756***
(0.639)
(1.023)
(0.623)
T2S2M1
-0.665
-2.528***
-1.652***
(0.533)
(0.565)
(0.402)
T2S4M1
-0.157
-2.226***
-1.216**
(0.614)
(0.689)
(0.488)
T2S4M2
-1.231**
-1.861**
-1.605***
(0.528)
(0.883)
(0.532)
T2S4M3
-0.538
-1.953**
-1.277**
(0.574)
(0.779)
(0.496)
T2S4M4
-0.707
-1.937***
-1.311***
(0.451)
(0.647)
(0.409)
T2S9M1
-0.374
-1.127*
-0.763*
(0.504)
(0.605)
(0.406)
T3S5M1
-0.564
0.00251
-0.152
(0.496)
(0.554)
(0.406)
T3S5M2
-0.625
-0.0954
-0.310
(0.814)
(0.690)
(0.540)
T3S5M3
-1.084*
-1.802*
-1.354**
(0.586)
(0.927)
(0.562)
T3S8M1
-0.651
-2.906***
-1.693***
(0.432)
(0.626)
(0.395)
T3S8M2
-0.589
-2.075***
-1.358***
(0.487)
(0.502)
(0.362)
T3S8M3
-1.130**
-3.409***
-2.218***
(0.518)
(0.517)
(0.383)
T4S6M1
-1.191**
-3.401***
-2.280***
(0.574)
(0.557)
(0.427)
T4S6M2
-0.643
-2.192***
-1.422***
(0.580)
(0.749)
(0.484)
52
Table E4 con d.
T4S6M3
-0.951**
-3.004***
-1.991***
(0.396)
(0.643)
(0.398)
T4S6M4
-1.032**
-2.364***
-1.684***
(0.460)
(0.587)
(0.383)
T4S7M1
-0.600
-2.494***
-1.557***
(0.814)
(0.653)
(0.550)
T4S7M2
0.197
-1.264*
-0.459
(0.581)
(0.755)
(0.481)
age_ma ke _mean
0.153
-0.132
-0.0195
(0.101)
(0.103)
(0.0709)
deg_ma ke _mean
-0.113
0.460
0.0887
(0.621)
(0.648)
(0.472)
exp_ma ke _mean
-0.273
-0.299
-0.217
(0.236)
(0.248)
(0.172)
in_ma ke _mean
0.326
-0.179
0.104
(0.397)
(0.437)
(0.288)
u _ma ke _mean
-0.217
-0.527
-0.378
(0.374)
(0.431)
(0.287)
gende _ma ke _mean
0.288
0.201
0.0636
(0.421)
(0.480)
(0.325)
Cons an
2.011
10.08***
6.809***
(2.341)
(2.445)
(1.642)
Obse a ions
270
270
540
Pseudo R2
0.0491
0.0806
0.0640
No es: The Di idend P ice RMSE is he Dependen Va iable. See No es o Table E1 o a iables’ de ini ion.
Appendix F
53
Wald es s o e he di e ence be ween he sums o ma ke dummy coe icien s belonging o
di e en ea men s. In o de o es o he null hypo hesis o absence o di e ences be ween
wo ea men s, we c onside :
𝐻0: 𝑍𝑟,𝑠 ≡∑βi,
𝑛𝑟
i=1 −∑βi,s
𝑛𝑠
i=1 =0
whe e and s iden i y he ma ke s associa ed wi h wo di e en ea men s. 𝑛𝑟 and 𝑛𝑠 a e he
numbe s o ma ke s belongi ng o ea men and s. Ou de sign includes six ma ke s o e ach
ea men . 𝑛𝑟 and 𝑛𝑠 a e he e o e always equal o six, excep o he ea men o which he
omi ed ca ego y o he model belongs (T ea men 1). No e ha he possibili y ha 𝑛𝑟>𝑛𝑠
o compa isons in ol ing T ea men 1 does no a ec he es ima ion o ou pai wise
compa ison s, since he omi ed ca e go y coe icien is implici ly ze o. Wi h e e ence o each
pai wise compa ison, ables om F1 o F12 epo he s a is ics 𝑍𝑟,𝑠 as well as he ela ed p-
alu e in b acke s (*** p<0.01, ** p<0.05, * p<0.1). In p a icula , each pai wise compa ison has
o be ead sub ac ing he colu mn a iable om he ow a iable, e.g. T1 – T2, T1 – T3, T1 –
T4, T2 – T3, and so on.
Table F1: Pai wise compa isons o Rmse E icien P ice ac oss ea men s in pe iods om 1 o 10
Rmse E icien P ice in Pe iods 1_10
T1
T2
T3
T4
T1
-0.16
(0.938)
-1.44
(0.444)
-2.34
(0.238)
T2
-1.28
(0.446)
-2.18
(0.292)
T3
-0.90
(0.617)
T4

54
Table F2: Pai wise compa isons o Rmse E icien P ice ac oss ea men s in pe iods om 11 o 20
Rmse E icien P ice in Pe iods 11_20
T1
T2
T3
T4
T1
2.02
(0.300)
-1.58
(0.384)
2.81
(0.136)
T2
-3.60*
(0.068)
0.79
(0.710)
T3
4.40**
(0.014)
T4
Table F3: Pai wise compa isons o Rmse E icien P ice ac oss ea men s in pe iods om 1 o 20
Rmse E icien P ice in Pe iods 1_20
T1
T2
T3
T4
T1
1.39
(0.327)
-1.37
(0.296)
0.63
(0.647)
T2
-2.77**
(0.031)
-0.76
(0.613)
T3
2.01
(0.120)
T4
55
Table F4: Pai wise compa isons o Rmse Bayes P ice ac oss ea men s in pe iods om 1 o 10
Rmse Bayes P ice in Pe iods 1_10
T1
T2
T3
T4
T1
0.39
(0.771)
-0.17
(0.871)
-1.41
(0.199)
T2
-0.57
(0.671)
-1.80
(0.200)
T3
-1.23
(0.292)
T4
Table F5: Pai wise compa isons o Rmse Bayes P ice ac oss ea men s in pe iods om 11 o 20
Rmse Bayes P ice in Pe iods 11_20
T1
T2
T3
T4
T1
-5.90***
(0.000)
-2.11**
(0.023)
-3.38***
(0.000)
T2
3.79***
(0.002)
2.52*
(0.057)
T3
-1.27
(0.192)
T4
56
Table F6: Pai wise compa isons o Rmse Bayes P ice ac oss ea men s in pe iods om 1 o 20
Rmse Bayes P ice in Pe iods 1_20
T1
T2
T3
T4
T1
-2.63***
(0.005)
-1.32*
(0.073)
-2.47***
(0.001)
T2
1.31
(0.162)
0.16
(0.867)
T3
-1.14
(0.138)
T4
Table F7: Pai wise compa isons o Rmse Unin o med P ice ac oss ea men s in pe iods om 1 o 10
Rmse Unin o med P ice in Pe iods 1_10
T1
T2
T3
T4
T1
3.07***
(0.001)
0.06
(0.939)
-2.17**
(0.013)
T2
-3.14***
(0.000)
-5.62***
(0.000)
T3
2.47***
(0.002)
T4
57
Table F8: Pai wise compa isons o Rmse Unin o med P ice ac oss ea men s in pe iods om 11 o 20
Rmse Unin o med P ice in Pe iods 11_20
T1
T2
T3
T4
T1
-4.93***
(0.000)
-3.89***
(0.000)
-8.29***
(0.000)
T2
0.40
(0.717)
-3.80***
(0.001)
T3
-4.21***
(0.000)
T4
Table F9: Pai wise compa isons o Rmse Unin o med P ice ac oss ea men s in pe iods om 1 o 20
Rmse Unin o med P ice in Pe iods 1_20
T1
T2
T3
T4
T1
-1.10
(0.168)
-1.96**
(0.011)
-5.39***
(0.000)
T2
-1.13
(0.138)
-4.56***
(0.000)
T3
-3.43***
(0.000)
T4
64
A he end o e ach pe iod you will be shown you indi idual gain s in he las
pe iod, and you accumula ed gains, al so he a e age gains in you g oup, he a e age
gains in you ma ke and he a e age gains o he membe s o he ype B g oup.