The evolution of reputation-based cooperation in regular networks

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 S anda d-Nu zungsbedingungen: Die Dokumen e au EconS o dü en zu eigenen wissenscha lichen Zwecken und zum P i a geb auch gespeiche und kopie we den. Sie dü en die Dokumen e nich ü ö en liche ode komme zielle Zwecke e iel äl igen, ö en lich auss ellen, ö en lich zugänglich machen, e eiben ode ande wei ig nu zen. So e n die Ve asse die Dokumen e un e Open-Con en -Lizenzen (insbesonde e CC-Lizenzen) zu Ve ügung ges ell haben soll en, gel en abweichend on diesen Nu zungsbedingungen die in de do genann en Lizenz gewäh en Nu zungs ech e. Te ms o use: Documen s in EconS o may be sa ed and copied o you pe sonal and schola ly pu poses. You a e no o copy documen s o public o comme cial pu poses, o exhibi he documen s publicly, o make hem publicly a ailable on he in e ne , o o dis ibu e o o he wise use he documen s in public. I he documen s ha e been made a ailable unde an Open Con en Licence (especially C ea i e Commons Licences), you may exe cise u he usage igh s as speci ied in he indica ed licence. h p://c ea i ecommons.o g/licenses/by/4.0/ 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 42. Milinski, M.; Semmann, D.; Bakke , T.C.M.; K ambeck, H.J. Coope a ion h ough indi ec ecip oci y: Image sco ing o s anding s a egy? P oc. R. Soc. B Biol. Sci. 2001,268, 2495–2501. [C ossRe ] [PubMed] 43. An onioni, A.; Cacaul , M.P.; Lali e, R.; Tomassini, M. Know hy neighbo : Cos ly in o ma ion can hu coope a ion in dynamic ne wo ks. PLoS ONE 2014,9, e110788. [C ossRe ] [PubMed] 44. Suzuki, S.; Kimu a, H. Indi ec ecip oci y is sensi i e o cos s o in o ma ion ans e . Sci. Rep. 2013 ,3, 1435. [C ossRe ] [PubMed] 45. Sasaki, T.; Okada, I.; Nakai, Y. Indi ec ecip oci y can o e come ee- ide p oblems on cos ly mo al assessmen . Biol. Le . 2016,12, 20160341. [C ossRe ] [PubMed] 46. Leima , O.; Hamme s ein, P. E olu ion o coope a ion h ough indi ec ecip oci y. P oc. R. Soc. B Biol. Sci. 2001,268, 745–753. [C ossRe ] [PubMed] 47. Panchana han, K.; Boyd, R. A ale o wo de ec o s: The impo ance o s anding o e olu ion o indi ec ecip oci y. J. Theo . Biol. 2003,224, 115–126. [C ossRe ] 48. Kando i, M. Social no ms and communi y en o cemen . Re . Econ. S ud. 1992,59, 63–80. [C ossRe ] 49. Pacheco, J.M.; San os, F.C.; Chalub, F.A.C. S e n-judging: A simple, success ul no m which p omo es coope a ion unde indi ec ecip oci y. PLoS Compu . Biol. 2006,2, e178. [C ossRe ] [PubMed] 50. Takahashi, N.; Mashima, R. The impo ance o subjec i i y in pe cep ual e o s on he eme gence o indi ec ecip oci y. J. Theo . Biol. 2006,243, 418–436. [C ossRe ] [PubMed] 51. Suzuki, T.; Kobayashi, T. E ec o ole ance o epu a ion-making no ms on co po a ion in social exchanges: An e olu iona y simula ion on social ne wo ks. Sociol. Theo y Me hods 2011,26, 31–50. 52. Nakai, Y.; Mu o, M. Eme gence and collapse o peace wi h iend selec ion s a egies. J. A i . Soc. Soc. Simul. 2008,11, 6. 53. Uchida, S. E ec o p i a e in o ma ion on indi ec ecip oci y. Phys. Re . E 2010 ,82, 036111. [C ossRe ] [PubMed] 54. Sigmund, K. The Calculus o Sel ishness; P ince on Uni e si y P ess: P ince on, NJ, USA, 2010. 55. Takahashi, N.; Mashima, R. The Eme gence o Indi ec Recip oci y: Is he S anding S a egy he Answe ? COE Wo king Pape 29; Hokkaido Uni e si y: Hokkaido, Japan, 2003; A ailable online: h p://lynx.le .hokudai. ac.jp/COE21/wo kingpape / (accessed on 14 Sep embe 2016). 56. Ho baue , J.; Sigmund, K. E olu iona y Games and Popula ion Dynamics; Camb idge Uni e si y P ess: Camb idge, UK, 1998. 57. Oh suki, H.; Iwasa, Y. Global analyses o e olu iona y dynamics and exhaus i e sea ch o social no ms ha main ain coope a ion by epu a ion. J. Theo . Biol. 2007,244, 518–531. [C ossRe ] [PubMed] 58. San os, F.P.; San os, F.C.; Pacheco, J.M. Social No ms o Coope a ion in Small-Scale Socie ies. PLoS Compu . Biol. 2016,12, e1004709. [C ossRe ] [PubMed] 59. Sigmund, K. Mo al assessmen in indi ec ecip oci y. J. Theo . Biol. 2012,299, 25–30. [C ossRe ] [PubMed] 60. Oishi, K.; Shimada, T.; I o, N. G oup o ma ion h ough indi ec ecip oci y. Phys. Re . E 2013 ,87, 030801. [C ossRe ] 61. Pollock, G.B.; Duga kin, L.A. Recip oci y and he e olu ion o epu a ion. J. Theo . Biol. 1992 ,159, 25–37. [C ossRe ] 62. Oh suki, H.; Iwasa, Y.; Nowak, M.A. Indi ec ecip oci y p o ides only a na ow ma gin o e iciency o cos ly punishmen . Na u e 2009,457, 79–82. [C ossRe ] [PubMed] 63. Wu, J.; Ballie , D.; Van Lange, P.A. Gossip e sus punishmen : The e iciency o epu a ion o p omo e and main ain coope a ion. Sci. Rep. 2016,6, 23919. [C ossRe ] [PubMed] 64. Yamagishi, T. The p o ision o a sanc ioning sys em as a public good. J. Pe sonal. Soc. Psychol. 1986 ,51, 110–116. [C ossRe ] 65. Sigmund, K.; de Sil a, H.; T aulsen, A.; Haue , C. Social lea ning p omo es ins i u ions o go e ning he commons. Na u e 2010,466, 861–863. [C ossRe ] [PubMed] 66. Sasaki, T.; Okada, I.; Uchida, S.; Chen, X. Commi men o coope a ion and pee punishmen : I s e olu ion. Games 2015,6, 574–587. [C ossRe ] 67. Han, T.A.; Lenae s, T. A syne gy o cos ly punishmen and commi men in coope a ion dilemmas. Adap . Beha . 2016. [C ossRe ] 68. Szolnoki, A.; Szabó, G.; Czakó, L. Compe i ion o indi idual and ins i u ional punishmen s in spa ial public goods games. Phys. Re . E 2011,84, 046106. [C ossRe ] [PubMed] Games 2017,8, 8 16 o 16 69. Ichinose, G.; Tenguishi, Y.; Tanizawa, T. Robus ness o coope a ion on scale- ee ne wo ks unde con inuous opological change. Phys. Re . E 2013,88, 052808. [C ossRe ] [PubMed] 70. Ishida, Y.; Yamamo o, H.; Okada, I.; O a, T. Robus ness and ulne abili y o coope a ion: Eme gence on ne wo k s uc u es. Compu . So w. 2007,24, 70–80. 71. Nakama u, M.; Kawa a, M. E olu ion o umo s ha disc imina e lying de ec o s. E ol. Ecol. Res. 2004 ,6, 261–283. 72. Ghang, W.; Nowak, M.A. Indi ec ecip oci y wi h op ional in e ac ions. J. Theo . Biol. 2015 ,365, 1–11. [C ossRe ] [PubMed] 73. Számadó, S.; Szalai, F.; Scheu ing, I. Decep ion unde mines he s abili y o coope a ion in games o indi ec ecip oci y. PLoS ONE 2016,11, e0147623. [C ossRe ] [PubMed] 74. An onioni, A.; Sánchez, A.; Tomassini, M. Coope a ion su i es and chea ing pays in a dynamic ne wo k s uc u e wi h un eliable epu a ion. Sci. Rep. 2016,6, 27160. [C ossRe ] [PubMed] 75. Seki, M.; Nakama u, M. Model o gossip-media ed e olu ion o al uism wi h a ious ypes o alse in o ma ion by speake s and assessmen by lis ene s. J. Theo . Biol. 2016 ,407, 90–105. [C ossRe ] [PubMed] © 2017 by he au ho s; licensee MDPI, Basel, Swi ze land. This a icle is an open access a icle dis ibu ed unde he e ms and condi ions o he C ea i e Commons A ibu ion (CC BY) license (h p://c ea i ecommons.o g/licenses/by/4.0/).