CULTURAL TRANSMISSION AND THE EVOLUTION OF TRUST AND RECIPROCITY IN THE LABOUR MARKET. Gonzalo Olcina and Vicente Calabuig

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1 Preliminr version o be published s Working Pper b BBVA Foundion CULTURAL TRANSMISSION AND THE EVOLUTION OF TRUST AND RECIPROCITY IN THE LABOUR MARKET Gonzlo Olcin nd Vicene Clbuig Universi of Vlenci nd ERI-CES ABSTRACT The lbour conrc ssigns usull significn uhori o he emploer (hierrchicl governnce). The hre of hold up of he emploee b he emploer, cused b his smmeric disribuion of decision righs, cn be miiged b preference for reciproci on he pr of he emploer or b blnce of power, rising from he credible hre b he emploee o relie if he is eploied. In his pper we invesige he inercion nd he evoluion beween he preferences for reciproci of he emploer nd he fesibili nd willingness o punish hosile behviour b he emploee in n overlpping generions model where here is culurl rnsmission of preferences. We chrcerize he long run behviour of his socie, h is, he sble sed ses of he dnmics. Our frmework shows how nd wh differen lbour culures or regimes cn resul in he long run. Our min resul ses h if he ne gins from specific invesmen re high enough nd he moun of fesible punishmen (i. e. he workers power) is lso high he econom will converge from n iniil condiion o n efficien cooperive equilibrium. If n of hese condiions does no hold, he mrke will sele down in n inefficien equilibrium where no ll pes of workers mke specific invesmen or lhough he do i, here is surplus desrucion becuse selfish firms offer low wges. Posiive reciproci on he pr of he emploers is no enough o chieve n efficien lbour culure. I is lso needed significn llocion of power o he workers in order o mke he hre of punishmen powerful ool o enhnce efficienc nd cooperion. Kewords: Culurl Trnsmission, Trus nd Punishmen, Lbour Power, Socil Preferences, Specific Invesmen. RESUMEN El conro de rbjo generlmene sign l mor pre de l uoridd l empresrio (gobernnz jerárquic). L menz de hold-up (oporunismo pos-conrcul) del empledor l empledo, cusd por es disribución siméric de los derechos de decisión, se puede miigr si eisen preferencis por l reciprocidd por pre del empresrio o se produce un equilibrio de poder, que surge de l menz creíble por pre del empledo de reli r represlis si es eplodo. En ese rículo se invesig l evolución l inercción enre ls preferencis por reciprocidd del empresrio l posibilidd el deseo de csigr un compormieno hosil, por pre del empledo, en un modelo de generciones solpds donde eise rnsmisión culurl de preferencis. En concreo, se crceriz el compormieno lrgo plzo de es sociedd, es decir, los esdos escionrios esbles de l dinámic. Ese nálisis muesr cómo por qué pueden surgir diferenes culurs lborles en el mercdo de rbjo. El resuldo principl que se obiene indic que si ls gnncis nes por relizr inversión específic

2 Preliminr version o be published s Working Pper b BBVA Foundion son lo suficienemene elevds l mgniud del csigo posible (el poder del rbjdor) mbién es lo, l economí convergerá desde culquier condición inicil un equilibrio cooperivo eficiene. Si culquier de ess condiciones no se cumple, el mercdo convergerá un equilibrio ineficiene, en el que, o bien, no odos los ipos de rbjdores hcen inversión específic o bien, unque l elijn, eise desrucción del ecedene porque ls empress egoíss ofrecerán slrios bjos un proporción de rbjdores los rechzrán. L presenci de reciprocidd posiiv por pre del empresrio no es suficiene pr conseguir un culur lborl eficiene. Tmbién se necesi signr los rbjdores suficiene poder pr que l menz de csigo se un rm poderos pr promover l eficienci l cooperción. Plbrs clve: Trnsmisión culurl, Confinz csigo, Poder del rbjdor, Preferencis sociles, Inversión específic.

3 Preliminr version o be published s Working Pper b BBVA Foundion. Inroducion Mos emplomen represens long-erm relionship beween he emploer nd he emploee. In mn of hese emplomen relions, boh gens re incresingl "ied" o one noher s he inves in relion-specific sses, wekening he discipline of mrke forces. The lbour conrc in hese cses is highl incomplee, involves imporn implici elemens nd i ssigns usull significn uhori o he emploer (hierrchicl governnce). However, he smmeric disribuion of uhori pus he emploee in dnger of being eploied, leding o inefficienc if he refuses o inves, or simpl refuses o coopere, fering h n such conribuion will go unreciproced. The hre of hold up of he emploee b he emploer cn be miiged b les hree mens oher hn b lw nd conrc provision: preference for reciproci on he pr of he emploer, blnce of power, rising from he credible hre b he emploee o relie if he is eploied nd finll, he desire of he emploer o minin repuion mong emploees for no being eploiive (see, for insnce, Bron nd Kreps, 999). In his pper we invesige he inercion nd he evoluion beween he preferences for reciproci of he emploer nd he fesibili nd willingness o punish hosile behviour b he emploee in n overlpping generions model where here is culurl rnsmission of preferences. More precisel, in our simplified lbour mrke, ech emplomen relion is chrcerized b he following sequence of evens: he worker hs o decide beween mking generl invesmen or specific or cooperive invesmen which resuls in higher surplus. Ne, he emploer ses wges nd hus, fer observing he emploees invesmen, he cn rewrd he cooperive cion of he emploee, ping high wge, or buse on him, ping low wge. Finll, he worker cn engge in cosl punishing civi, desroing pr of he surplus. Thus, plers re fcing one-sided sequenil Prisoners Dilemm wih finl punishmen sge. We represen he smmeric disribuion of uhori b ssumming h he emploer cn

4 Preliminr version o be published s Working Pper b BBVA Foundion eploi or hold up on he worker b ppropiing ll he surplus derived from cooperion, while he worker lcks his cpci wih respec o he emploer. Noice h our noion of uhori is differen from oher definiions used in he lierure (for insnce, Simon, 95 or Aghion nd Tirole, 997). On he oher hnd, we represen he possible relior power of he workers b mens of punishmen sge: he fesibili o punish hosile behviour b desroing surplus ("mone burning"). Noice h in order o mke credible hre of reliion i is no enough wih he willingness o punish hosile behviour, bu i is lso needed h he rules of he gme (he insiuions) llow for sufficien moun of cosl punishmen. In fc, our min ineres in his work lies in he inercion beween he evoluion of he preferences for reciproci nd he insiuionl feures h mke possible he relior power of he emploees. If he bove gme is pled b he usul selfish gens of convenionl economic heor, i will resul in n inefficien oucome: he emploee chooses generl invesmen nd i is obined low surplus. A cosl punishmen is no credible hre b selfish worker. Therefore, he worker cnno rus n promise mde b he selfish emploer of being rewrded in cse he mkes he specific invesmen. Obviousl, repuion is well-known soluion o his inefficienc in repeed scenrio, even if he gens re selfish. Neverheless, s we wn o isole he influence of firness nd he blnce of power on he efficienc of he emplomen relions, we will ssume h he bove gme is pled onl once in n emplomen relion in order o elimine n possible influence of he repuion moive. I is well-known h firness concerns m hve decisive impc in he cul working of he lbour mrkes (see Fehr nd Gcher, 000, 000b). Fir-minded gens will ehibi reciproci in heir observed behviour. B reciproci we men he H. Simon, 95: "We will s h (he boss) eercises uhori over (he worker) if (he worker) permis (he boss) o selec ( behvior, i.e., n elemen of he se of specific cions h he worker performs on he job...". 3

5 Preliminr version o be published s Working Pper b BBVA Foundion willingness o rewrd friendl behviour nd he willingness o punish hosile behviour. If he bove emplomen gme is pled b fir-minded gens or lernivel, here is high proporion of his pe of gens in boh populions of emploers nd emploees, he resuling oucome would be he efficien one. Th is, workers mke specific invesmens nd emploers reciproce wih high (fir) wges. We wn o nlze wheher hese preferences cn survive in culurl compeence wih he convenionl selfish preferences (i.e. gens who r o mimize heir meril poffs). For his purpose, we work wih dnmic model of culurl rnsmission, where boh he disribuion of preferences in he populion nd he sregies in he lbour mrke in he long run re deermined endogenousl nd simulneousl. Preferences in boh populions of emploers nd emploees re heerogeneous. In ech period here is frcion of selfish gens, nd here is lso frcion of gens moived b reciprocl lruism. The disribuion of preferences in he populion evolves ccording o process of culurl rnsmission which combines direc rnsmission from prens wih oblique rnsmission from he socie (Cvlli-Sforz nd Feldmn, 98, Bod nd Richerson, 985). Prens mke cosl decision on educion effor ring o rnsmi heir own preferences (Bisin nd Verdier, 00). If he do no succeed, children cquire preferences from he socil environmen. In conrs wih oher models, where oblique rnsmission kes plce in socie lrge, we ssume h economic gens re socilized eclusivel wihin heir prens socil clss. Emploers children re socilized, eiher b heir prens or b oher dul emploers. And he sme ssumpion pplies o emploees. We denoe his siuion s segmened or "clssis" socie. We chrcerize he long run behviour of his socie, h is, he sble sed ses of he dnmics. As firs resul we obin h in n of hese sed ses here is heerogenous disribuion of preferences in he populion of boh socil clsses. More ineresingl, our frmework shows how nd wh differen lbour culures or regimes cn rise in he long run. And lso in which cses here eiss muliplici of sed ses, depending he finl oucome on he iniil condiion (he hisor) of he 4

6 Preliminr version o be published s Working Pper b BBVA Foundion socie. Nmel, four lbour regimes cn persis in he long run. A ver efficien one in which boh pes of workers nd boh pes of emploers coopere in " gifechnge" (Akerlof) w. All workers mke specific invesmen, ll emploers p high wges nd here is no surplus desrucion. A second one, in which boh pes of workers mke specific invesmens, bu selfish emploers p low wges nd re punished b fir-minded workers, while fir-minded emploers offer high wges. A hird regime in which onl selfish workers mke specific invesmen, while fir-minded workers choose o mke generl invesmen. And finll, he lbour mrke cn ge rpped in he inefficien oucome in which boh pes of workers mke generl invesmens wih populion wih ver high proporion of selfish emploers. Our nlsis shows h if he ne gins from mking specific invesmen re high enough nd he workers power, mesured b he miml moun of surplus he re ble o desro, is lso sufficienl high, he econom will converge from n iniil condiion o he efficien Akerlof-pe equilibrium. On he oher hnd, wih high ne gins from specific invesmen bu low workers power or ver high cos of punishmen, he mrke will sele down in n inefficien equilibrium. In his equilibrium no ll pes of workers mke specific invesmen or lhough he mke i, here is surplus desrucion becuse selfish firms offer low wges. Onl if boh he ne gins from cooperion nd he workers power re ver low, he mrke will ge rpped in he ver inefficien equilibrium in which boh pes of workers mke generl invesmen. Posiive reciproci (rewrding) on he side of he emploers is no enough o chieve n efficien lbour culure. Trus nd gif echnge operes in he mrke onl if here is blnce of power. Or, in oher words, under he shdow of credible hre of significn punishmen. I is needed sufficien llocion of relior power o he workers in order o mke he hre of punishmen powerful ool o enhnce efficienc nd cooperion. There re some few works reled o our pper. Herold (004) presens n indirec evoluionr pproch o nlze gme in which pler chooses beween cooperion or defecion nd second pler cn rewrd or no his cooperion nd cn punish or no his defecion. This uhor sudies he evoluion of reciproci preferences 5

7 Preliminr version o be published s Working Pper b BBVA Foundion for rewrding nd preferences for punishing in compeiion wih purel self-ineresed preferences. Our pproch is differen. On he one hnd, Herolds evoluionr dnmics is poff monoonic s i is usul in n evoluionr model. In our model, he culurl dnmics is no necessril poff monoonic becuse i is bised b he culurl inolernce of he prens. On he oher hnd, he srucure of our gme is differen: in our cse cooperion cn be rewrded or no b he emploer nd hen, non-rewrding cn be punished or no b he emploee. We hink h our sequence of evens is much more well-suied s represenion of hierrchicl lbour relionship, in which here is blnce of power. Fehr, Klein nd Schmid (007) presen robus eperimenl evidence showing h conrcs h offer volunr bonus for sisfcor performnce provide superior incenives h eplici incenive conrcs nd lso h rus (Akerlof) conrcs. In bonus conrc, boh plers cn muull reciproce: he firm ps wge upfron, he worker eers effor nd he firm cn rewrd him ping n unenforceble bonus. So his gme represens nurl benchmrk for mking comprison beween he power of punishmen nd he power of muul reciproci in order o enhnce efficienc. I urns ou h punishmen is more powerful ool. In heir model, full efficienc is no rechble: selfish emploers will no p bonus nd, niciping his, fir-minded emploees provide low effor. In our model, provided he fesibili of engging in cosl punishmen of he workers is high enough, full efficienc is reched. All workers mke specific invesmen nd ll firms p high wges, given he credible hre of punishmen. There is lo of empiricl work nlzing he economic impc of workers power (unions, legl righs, lbour sndrds nd so on). Freemn nd Medoff (984) in clssicl work show mong oher hings, how on verge, unions cree bigger pie o be spli beween he workers nd he owners of he firms. However, here is conrdicor evidence on hese issues (see Menezes, 997). There lso eiss few heoreicl pproches s, for insnce, Almn (000). In his work, he uhor shows, using sic behviourl model, how n increse in lbour power cn be welfre enhncing in mrke econom. The res of he pper is orgnized s follows. Secion presens he emplomen relionship. Secion 3 inroduces he inequi version preferences nd nlzes he 6

8 Preliminr version o be published s Working Pper b BBVA Foundion behviour of inequi verse gens. Secion 4 sudies he emplomen gme wih heerogeneous preferences in boh populions. Secion 5 summrizes he mechnism of culurl rnsmission of preferences. Secion 6 nlzes he dnmics of he segmened or wo-clss socie. In secion 7, we chrcerize he sed ses or long run lbour culures under he culurl dnmics nd heir bsins of rcion. Finll, secion 8 concludes.. The emplomen relionship We consider overlpping generions of gens who onl live wo periods (s oung nd s n dul). The gens cn be workers or owners of firms (emploers), nd we ssume h ech pe of gen belongs o "socil clss" or group. In he firs period, he gen is child nd is educed in cerin preferences, nd in he second period, he gen (s n dul wih well-defined preferences), is rndoml mched wih n dul pler from he oher "clss" or group, o pl he sge gme o be described ler. In his second period, n dul pler hs one offspring nd hs o mke (cosl) decision regrding his/her child educion, ring o rnsmi his/her own preferences. As i is cusomr in his clss of models we will ssume h n dul hs jus one child independenl of he poffs in he sge gme, nd hus he populion remins consn. I is lso ssumed h reproducion is seul, wih pren per child. The sge gme Two dul plers drwn from ech "socil clss" re rndoml mched o pl he following sequenil gme. The worker (he, pler ) hs o decide wheher o mke specific invesmen (S) or generl invesmen (G). If he chooses generl invesmen, i is obined nonnegive surplus of size l, where for simplici, we ssume h is divided equll beween he emploer (she, pler ) nd he worker, nd he gme ends. 7

9 Preliminr version o be published s Working Pper b BBVA Foundion If he worker chooses o mke specific invesmen, i is produced ol surplus of H, higher hn l. Ne, he firm ses wges. Therefore, fer observing S, she hs o decide which proporion b [ Î 0,] of H she is willing o p o he worker. In order o simplif he nlsis, i is ssumed h he offer b = 0 covers he cos for he worker of mking specific invesmen. The worker, fer observing b, hs he opion of punishing he firm, desroing proporion λ of H ( b) some unir cos z. If he decides no o punish, he firm ges poff of H ( b) nd he worker poff of bh. If he decides o punish, he firm obins poff of H ( b λ ( b)) nd he worker ges poff of H ( b zλ ( b)). We denoe λ s he miml punishmen h he worker cn inflic on he emploer. For emple if λ =, he worker cn desro ll he surplus of he firm. We denoe his prmeer s he srengh or he power of he workers. I depends on he workers bili for mone burning (sboge, srikes,.. ) which in urn migh depend on he workers degree of unionizion, heir bili o orgnize collecivel, heir legl righs in he socie... I lso differs cross differen pes of jobs depending on he sregic posiion of he worker in he producion process. On he oher hnd, he cos of his civi of mone burning (unir cos z ) vries wih he firms cpbili of finding ou nd sncioning his civi in cse of sboge or wih he difficul of coordinion nd orgnizion in cse of srikes. However, in his pper we will ssume he sme prmeers λ nd z for ll workers. We lso ssume h his miml punishmen hs o sisf he resricion / λ. This ssumpion on he lower bound will be jusified ler on. Wih his sge gme we wn o model siuion h reflecs, on he one hnd, h he worker runs he risk of being held up, in cse he firm does no rewrd his cooperive cion, nd on he oher hnd, he blnce of power cpured b he punishmen opion or hreened dmge h he worker cn inflic on he firm. Suppose now h ll plers hve self-regrding preferences nd here is complee informion. We cn obin he Subgme Perfec Equilibrium solving he gme b bckwrd inducion. In he ls subgme, selfish workers do no punish 8

10 Preliminr version o be published s Working Pper b BBVA Foundion becuse i is cosl nd does no increse heir poff. Given h he firm will no be punished, she will offer proporion b = 0 o he worker nd herefore he opiml cion for him will be o mke generl invesmen he beginning of he gme. This is n inefficien oucome in which boh plers obin he sme poff, i.e., l. In his sequenil sge gme, boh he promise of rewrding b he firm nd he hre of punishmen b he worker re no credible. In his pper we will ssume h here is heerogenei of preferences, nd h in ddiion o self-regrding people here is lso significn frcion of he populion h ehibis socil preferences, h is, he re lso concerned b relive poffs. In he ne secion we will inroduce his pe of preferences. 3. Socil preferences: Inequi version There is nowds n overwhelming evidence from eperimenl d showing h significn frcion of he subjecs does no cre onl bou meril poffs bu rher relive poffs. These eperimens nd lso everd's eperience, sugges h firness nd reciproci moives ffec he behviour of mn people. In our pper he disribuion of preferences in boh populions of economic gens in ech period is endogenousl deermined b he decision mde b dul plers. In ech "socil" clss or group, here is cerin proporion of people wih selfish preferences nd he remining proporion wih reciprocl preferences. In priculr, in he workers (firms ) populion here is proporion ( ) of selfineresed gens in period who re moived eclusivel b heir own moner poffs nd proporion ( ) of gens who ehibi reciproci in heir observed behviour. A number of heoreicl models hve been developed in he lierure o obin reciprocl behviour. Well-known emples include Fehr nd Schmid (999) nd Bolon nd Ockenfelds (000) s models of inequi version, Chrness nd Rbin (00) s model of qusi-mimin preferences, Rbin (993) nd Dufwenberg nd 9

11 Preliminr version o be published s Working Pper b BBVA Foundion Kirchseiger (004) s models of inenion-bsed reciproci. These models cn led o differen predicions in some priculr gmes, bu in our sequenil prisoners dilemm he ll deliver reciprocl behviour. For rcbili resons, we choose in his work he inequi version preferences model of Fehr nd Schmid (999) bu he resuls would no chnge quliivel wih n oher pe of efficienc-enhncing socil preferences s hose previousl menioned. Le m = ( m, m ) denoe he vecor of moner poffs for boh plers. The uili funcion of n inequi verse pler i is given b: Ui ( m) = mi α m{ m j mi,0} β m{ mi m j,0}, j i, where β α nd > β 0. Inequi verse gens re willing o give up some meril poff o move in he direcion of more equible oucomes. The second erm in he bove epression mesures he uili loss from disdvngeous inequi, while he hird erm mesures he loss from dvngeous inequi. The ssumpion β α implies h pler suffers more from inequi h is o his disdvnge, h is, he inequi version is smmeric. We lso ssume h β > 0.5 nd denoe his pe of plers s srongl inequi verse plers. Srongl inequi verse plers hve ver differen policies s compred o hose of selfish plers, in priculr he rewrding polic of he emploers nd he punishing polic of workers. The inequi verse emploers compense generousl he cooperive cion of he workers nd he inequi verse workers re willing o punish low rewrding polic b he firms, provided h he uni cos of punishmen is low enough. Le us prove hese policies in urn. 3.. Punishmen polic of srongl inequi verse workers In conrs o he behviour of selfish workers, he hre of punishmen is credible in he cse of inequi verse workers, provided h he uni cos of punishing 0

12 Preliminr version o be published s Working Pper b BBVA Foundion z is smller hn criicl vlue which is incresing in α, he prmeer h cpures his degree of disdvngeous inequi version. α Lemm Assume z, if he inequi verse worker is offered rewrd + α b / b he firm, he will no punish her. If he firm offers rewrd b < /, he worker will punish her wih punishmen h depends inversel on he compension offered b he firm. In priculr, if he worker is offered rewrd of b, λ + λ z 0 b b =, λ + λ z punishmen. where he will punish he firm choosing λ, he miml possible If he worker ges n offer b, where b < b < /, b choosing λ = < λ. ( z)( b) he will punish he firm Proof. See Appendi. The inuiion behind his resul is h b punishing, he inequi verse worker, reduces inequli gins him nd his posiive effec more hn compenses he diminuion in his meril poffs. Noice h in principle, he inequi verse worker will punish his opponen unil n eglirin poff vecor is obined. Bu if he wge offer of he emploer is ver smll, n eglirin poff is no fesible becuse here is limi in he moun of punishmen λ. And in his cse, he worker punishes unil his limi is reched. 3.. Rewrding polic of srongl inequi verse emploers A srongl inequi verse firm hs dominn sreg which is o offer hlf of he surplus (b = /) o he worker. This sreg implies h none of boh pes of worker will punish her. Noice h sring in n unequl dvngeous disribuion for her, o give one moner uni o he worker reduces her meril poff in one uni nd

13 Preliminr version o be published s Working Pper b BBVA Foundion consequenl her uili. Bu, i lso reduces he inequi in wo unis. Therefore, s β > 0.5, her uili increses in more hn one uni. The ol effec is n increse in her uili. We relege o he Appendi more forml proof Chnges in he behviour of selfish gens The presence of inequi verse gens in he populion induces chnges in he behviour of selfish gens. For insnce, selfish worker who fces n inequi verse firm wih probbili one will choose o mke specific invesmen, becuse he knows h he firm will offer n equible rewrd. The behviour of selfish emploer will lso depend crucill on he pe of worker h she fces. We lred know h when selfish firm fces wih probbili one selfish worker, she will offer no rewrd niciping h his pe of pler does no punish. Bu when selfish firm fces srongl inequi verse pler wih cerin, her rewrding polic will chnge subsnill. In priculr, she will offer b = /, becuse she nicipes h he will punish her if she does no offer n equible rewrd.this resul is sed in he following lemm. Lemm A selfish emploer fced wih probbili one wih n inequi verse worker, will offer wge of b = /. Proof. See Appendi. As consequence, he inequi verse worker, niciping his behvior of he emploer, will choose o mke specific invesmen, ielding he efficien oucome, surplus of size H. Noice h his lemm onl holds for λ /. If he workers' srengh λ is smller hn /, h is, he workers cn onl desro mos less hn hlf of he surplus, he opiml behviour of selfish emploer is o offer b = 0. Thus, her behviour would be he sme h in bsence of he punishmen opion. This eplins our ssumpion on he lower bound on λ.

14 Preliminr version o be published s Working Pper b BBVA Foundion Summrizing, if i is common knowledge h boh, or les one of he gens is inequi verse, hen he worker mkes specific invesmen nd he emploer rewrds him wih high wge. Boh he firm nd he worker will ge poff of H /. The inuiion behind hese resuls is he following. When he firm is n inequi verse pler she behves generousl in her rewrd polic offering b = /. Then, he selfish worker does no fer being eploied. On he oher hnd, s inequi verse workers re willing o punish n offer below b = /, selfish firms, niciping his behvior, will behve lso generousl offering hlf of he surplus. Therefore, he inequi verse pler will choose he sr of he gme o mke specific invesmen, chieving he efficien oucome. Bu noe h plers do no know he rue pe of he pler wih whom he re mched wih in period. However, we will ssume h he know he preferences disribuion or in boh socil "clsses" or groups. We will sud his incomplee informion gme in he ne secion. 4. Trus nd punishmen wih heerogeneous preferences In his secion, we chrcerize he Perfec Besin Equilibri of he incomplee informion sequenil gme pled in ech period. Th is, neiher pler knows he rue pe of pler h he is rndoml mched wih bu he know he disribuion of preferences of he populion from which pler is drwn. This disribuion of preferences will be endogenousl deermined in our model b he educion decisions mde b dul plers. Noice, firs, h he rewrding polic of n inequi verse firm does no chnge when here is incomplee informion. However, he rewrding polic of selfish firm is indeed ffeced b he eisence of frcion of inequi verse workers. To compue he opiml rewrding polic of selfish emploers, noe h he priculr decision mde b he worker migh lso chnge her beliefs bou he worker's 3

15 pe. We will denoe b Preliminr version o be published s Working Pper b BBVA Foundion μ ( e / S) he upded probbili in period which he firm ssigns o he worker being selfish fer observing he cion S. Then, he selfish firm hs hree opions: i) o offer low wge b, such h 0 b < b, ii) o offer n inermedie wge b, such h b b < / or, finll, iii) o offer generous rewrd, b = /. We show in he Appendi h he second opion is domined b he oher wo. I is es o see h if he firm wishes o offer low wge, he bes opion is o se b = 0. Thus, we hve o compre wheher he firm prefers o offer b = 0 or b = /. The nswer depends obviousl on he beliefs bou he proporion of selfish workers in he populion. In he following lemm we se his resul: Lemm 3 A selfish emploer will use he following rewrding polic: λ / ) Offer b = 0 if μ > λ λ / b) Offer b = / if μ λ Proof. See Appendi Now we re red o obin he se of Perfec Besin Equilibri of his incomplee informion gme. Firsl, we will check he eisence of sepring equilibri in which he wo pes of workers choose differen kind of invesmens. sep Lemm 4 Sepring equilibrium e. For ever nd '' [, %, ] where '' H l H (+ ( zλ (+ α) + α( λ )) = H- l % =, here eiss Perfec Besin Equilibrium (PBE) in which he selfish H worker chooses o mke specific invesmen (S) nd he inequi verse worker chooses o mke generl invesmen (G). The selfish firm offers b = 0 nd he inequi verse nd 4

16 Preliminr version o be published s Working Pper b BBVA Foundion firm offers b = /. The equilibrium poff of he selfish worker is ( ) H/, for he inequi verse worker is l, for he selfish firm is H + ( ) l nd for he inequi H verse firm is + ( ) l. Proof. See Appendi. Noe h, prdoicll, in his inefficien equilibrium, selfish workers mke specific invesmen nd srongl inequi verse workers mke generl invesmen. The reson is h he former pl cooperivel becuse of he presence of significn frcion of fir-minded emploers who p high wges. And he ler choose generl invesmen becuse of he presence of significn frcion of selfish emploers who p low wges. As he punishmen is cosl, if he number of selfish firms is high enough, i is no worhwile for he inequi verse worker o mke specific invesmen. '' This eplins h his equilibrium onl eiss for n inermedie rnge of Î [, % ]. Th is, if here were oo few fir-minded emploers, selfish workers would no find profible o mke specific invesmen nd if here were oo mn fir-minded emploers, hen inequi verse workers would mke specific invesmen. Noe lso h here is no sepring equilibrium in which selfish worker chooses G nd n inequi verse worker chooses S. In his cse, emploers would offer high wges (b = /), nd selfish workers would devie, imiing he behviour of heir inequi verse mes. Ne, we will show severl lemms h chrcerize he pooling equilibri of his gme in which boh pes of workers choose he sme pe of invesmen. We begin wih equilibri in which here is specific invesmen. p Lemm 5 Pooling equilibrium e. A similr resul is obined in Fehr, Klein nd Schmid (007) in principl gen model. The presence of fir principls induces selfish gens o choose high effor levels, while he presence of selfish principls induces he fir gens o provide low effor levels. 5

17 Preliminr version o be published s Working Pper b BBVA Foundion l - / For ever nd [0, ˆ Î ], where ˆ =, here eiss PBE in which l boh pes of workers choose o mke specific invesmen ( S ) nd boh pes of firms choose o offer b = /. The equilibrium poff for ll plers is H /. Proof. See Appendi. This is he efficien equilibrium of he gme. All pes of workers mke specific invesmen nd ll pes of emploers p high (fir) wges nd herefore, here is no surplus desrucion. A relivel high frcion of inequi verse workers is needed for he eisence of his equilibrium. This pe of workers credibl punishes he unfir behviour of emploers. Thus, if is proporion is high enough, selfish emploers re beer off offering high wges nd voiding punishmen. Noice h he criicl frcion of selfish workers ˆ depends posiivel on he workers' power λ nd cn ke vlues beween 0 nd /. Bu here is lso second pooling equilibrium in which boh pes of workers mke s well specific invesmen bu he selfish emploer is no so generous, s i is sed in he following lemm: p Lemm 6 Pooling equilibrium e. For '' Î [ ˆ,] nd Î é0, ù ê ë ú û, here eiss PBE in which boh pes of worker choose o mke specific invesmen (S), he selfish firm offers b = 0 nd he inequi verse firm offers b = /. The equilibrium poff of he selfish worker is ( ) H/, for he inequi verse worker is ( ) H/ + ( zλ H α( H λ H + zλ H ) (while his meril poff is ( ) H/ ( zl H), for he selfish firm is H + ( )( H λ H ) nd for he inequi verse firm is H. Proof. See Appendi. Noice h his is n inefficien equilibrium becuse fir-minded workers punish he low wges offered b selfish emploers desroing he miml possible moun of 6

18 Preliminr version o be published s Working Pper b BBVA Foundion surplus. This equilibrium eiss in lbour mrke wih high proporion of selfish workers nd low proporion of selfish emploers. A high proporion of selfish workers is needed for selfish firms o offer low wges nd low proporion of selfish firms is needed for inequi verse workers o mke specific invesmen, given h punishmen is cosl. Finll, here is lso ver inefficien equilibrium in which boh pes of workers mke generl invesmen. pg Lemm 7 Pooling equilibrium e. H- l For ever nd Î [%,], where % =, here eiss PBE in which H boh pes of worker choose o mke generl invesmen (G ). The off-equilibrium beliefs h suppor his equilibrium re m (/ )> ˆ es. The equilibrium poff for ll plers is l. Proof. See Appendi. Noice h his equilibrium rises in lbour mrke wih ver high proporion of selfish emploers. The criicl vlue % depends on he ne gins of efficienc derived from mking specific invesmen. The greer re hese gins, he higher is his criicl vlue. The emploers' beliefs in his equilibrium re such h if he observe specific invesmen he will infer h his cion is more likel o come from selfish worker. 5. The socilizion process nd he educion effor b prens in segmened socie Humn behviour is governed b preferences h re rnsmied hrough generions nd cquired b lerning nd oher ws of socil inercion. The rnsmission of preferences which is he resul of socil inercion beween generions 7

19 Preliminr version o be published s Working Pper b BBVA Foundion is clled culurl rnsmission. We will drw from he model of culurl rnsmission of Cvlli-Sforz nd Feldmn (98) nd Bisin nd Verdier (00). Prens purposeful nd cosl socilizion deermines he disribuion of preferences in boh populions of emploers nd emploees. Children cquire preferences hrough observion, imiion nd lerning of culurl models previling in heir socil nd culurl environmen, h is, in heir fmil nd in heir socil group. i Le Î [0,] be he educionl effor mde b pren of clss j of pe i j where j {,}, denoes worker nd emploer nd where i { e, }, e denoes selfish nd denoes srongl inequi verse. The socilizion mechnism works s follows. Consider pren wih i preferences. His child is firs direcl eposed o he pren's preferences nd is socilized o his preferences wih probbili i j chosen b he pren (vericl i rnsmission); if his direc socilizion is no successful, wih probbili -, he is socilized o he preferences of role model picked rndom in populion composed eclusivel of members of he sme "socil clss" (oblique rnsmission). In his ler spec we depr from he usul pproch in which oblique rnsmission kes plce in socie lrge. We cll his process s he socilizion process in segmened or "clssis" socie. ik Le P j denoe he probbili h child of pren of socil clss j wih preferences i is socilized o preferences k. The socilizion mechnism in clss j is hen chrcerized b he following rnsiion probbiliies where v is he proporion of selfish pes in his socil clss (v is for workers nd for emploers): P P P P = + - ( ) ee e e j j j e ( )( v) ( )( v) = - - e j j j j j ( ) v e j j v = = - j 8

20 Preliminr version o be published s Working Pper b BBVA Foundion Given hese rnsiion probbiliies i is es o chrcerize he dnmic behvior of v : v é êë v P ( v) P ee e + = j + - j ù úû Subsiuing we obin he following equion on differences: v v v( v) é ëê e + = + - j - j ù úû Noe h his culurl rnsmission mechnismcombines direc purposeful rnsmission wih oblique rnsmission. Direc rnsmission is jusified becuse prens re lruisic owrds heir children. Bu, n imporn feure is h he hve some kind of imperfec lruism: heir socilizion decisions re no bsed on he purel meril poff epeced for heir children bu on he poff s perceived b heir prens ccording o heir own preferences. This priculr form of mopi is clled imperfec emph (Bisin nd Verdier, 00). As consequence, he culurl dnmics is no necessril poff-monoonic. Direc rnsmission is lso cosl. Le C( i j) denoe he cos of he educion effor i, j Î {,} nd iî { e, } j. While i is possible o obin similr resuls wih n incresing nd conve cos funcion we will ssume, for simplici, he following C i i qudric form ( ) ( ) / i chooses he educion effor { 0,} j = q, wih q > 0. Therefore, pren from clss j of pe i j Î ime, which mimizes j ( ) ( ) ( ) ( ) ( ) P ii i, v V ii v E P ik i, v V ik v E i /q j j j j j j j Where P ij re he rnsiion probbiliies nd ik V j is he uili o pren of clss ik E j wih preferences i if his child is of pe k. Noice h he uili V j depends on v +, which denoes he epecion bou he proporion of selfish plers in period + in our own socil clss. In his work we will ssume h prens hve dpive or 9

21 Preliminr version o be published s Working Pper b BBVA Foundion bckwrd looking epecions, believing h he proporion of selfish plers will be E he sme in he ne period h in he curren period, h is, v = + v. Mimizing he bove epression wih respec o i, j Î {,} nd i { e, } ge he following opiml educion effor funcions 3 : () v = q D V ( v ) (- v ) e e j j () v = q D V ( v ) v j j Here Δ V = V V nd e j ee j e j Δ V = V V. Th is, j j e j j Î we i Δ V j is he ne gin from socilizing our child o our own preferences. I cn lso be inerpreed s he culurl inolernce of prens wih respec o culurl deviion from heir own preferences. According o he imperfec emph noion, prens obin higher uili if heir children shre heir preferences, so hese levels of culurl inolernce re non-negive. In he following secion we compue hese levels nd he dnmics of preferences in boh groups or socil clsses. 6. Dnmics of he preferences disribuion in segmened socie In his secion we will chrcerize he dnmics nd he possible sed ses of he econom for segmened socie, h is, socie wih complee segregion or culurl seprion beweeen he wo socil clsses. Boh socil groups coordine in n equilibrium of he sequenil gme nd herefore, given heir dpive epecions, he believe h his equilibrium will be pled b he ne generion. We need o know he opiml level of educion h prens choose in ech period. In order o do so we hve 3 In order o hve inerior soluions he prmeer q mus be chosen smll enough so h in equilibrium τ <. i j 0

22 Preliminr version o be published s Working Pper b BBVA Foundion o compue he ne gins for prens of rnsmiing heir own preferences h re given ik b epression V. j In order o simplif he nlsis we will ssume h he low surplus is zero (l = 0). In his cse, he pooling equilibri in which boh workers choose G, onl eiss for ever nd for =. We will commen in noher secion he consequences of reling his simplifing ssumpion. Now we cn divide he spce of pirs of populion preference disribuions (, ) in four regions. Region is chrcerized b ³ nd ˆ. In his region here is muliplici of equilibri: he pooling equilibrium sep e. p e nd he sepring equilibrium Region is chrcerized b nd ˆ. In his region here is unique p equilibrium: he pooling equilibrium e. Region 3 is chrcerized b ³ nd ³ ˆ. In his region he onl sep equilibrium is he sepring equilibrium e. Finll, region 4 is chrcerized b nd ³ ˆ. In his region here is p lso unique equilibrium: he pooling equilibrium e. We displ grphicll hese regions in figure.

23 Preliminr version o be published s Working Pper b BBVA Foundion Noice h in region here is muliplici of equilibri. If he mrke is in his region, we will ssume h ll gens epec nd coordine in he Preo dominn p equilibrium, nmel, he e equilibrium. Noice h for l = 0 ll pes of boh groups of gens obin higher meril poff in his equilibrium hn in he sepring p equilibrium. Moreover, he e equilibrium is more eglirin, herefore, he uili of ll pes is higher The dnmics of preferences when gens coordine in he equilibrium In his cse, which comprises regions nd, he proporion of selfish workers ˆ nd prens (workers nd emploers) pl in he populion is relivel smll ( ) p nd epec o be pled he equilibrium e, in which boh pes of workers choose o mke specific invesmen (S) nd boh pes of firms choose o offer b = /. Noice h V ik j = H/ for ll pes of prens. Therefore, he ne gins for n pe of pren of n socil clss obined from rnsmiing heir own preferences p e 4 This resul holds lso for l > 0 whenever λ ( H l)/ H.

24 Preliminr version o be published s Working Pper b BBVA Foundion ik Δ V j, h is, heir levels of culurl inolernce, re zero. Bu his in urn implies h here re no incenives ll for socilizion for n pren. Therefore, ll he opiml educion effor funcions re zero nd consequenl, he disribuion of preferences in boh populions will remin unchnged, h is + = nd + =. Summrizing, in his cse here re no incenives o socilize nd ech of he wo populions remins locked in he iniil disribuion of preferences. Therefore, n iniil disribuion of preferences in his region is sble sionr se of he p dnmics where he equilibrium e is pled. 6.. The dnmics of preferences when gens coordine in he equilibrium For clri in he eposiion we will run iniill he nlsis for his cse for ll he regions where he e sep equilibrium eiss. Th is, regions nd 3, where > ³ nd hus, he proporion of selfish emploers is relivel high. In his equilibrium he selfish worker chooses o mke specific invesmen (S) nd he inequi verse worker chooses o mke generl invesmen(g). The selfish firm offers b = 0 nd he inequi verse firm offers b = /. In his cse, ll pes of prens hve sricl posiive levels of culurl inolernce nd consequenl, he will hve incenives for cive socilizion. For emple, selfish worker pren epecs h when his child urns ou o be selfish will obin n epeced poff of ( ) H/ nd when his child urns ou o be inequi verse will obin poff of zero. Therefore, he selfish pren hs posiive level of culurl inolernce wich depends on ( ), he proporion of inequi verse emploers, nd on H, he gins from cooperion. The precise clculion of ll hese levels of culurl inolernce nd he opiml educion effor funcions for boh pes of workers is releged o he Appendi. Subsiuing hese funcions in he equion on differences of secion 5 nd using he ssumpion of bckwrd looking epecions, we ge he following dnmics for he workers disribuion of preferences : 3 sep e

25 Preliminr version o be published s Working Pper b BBVA Foundion + e = + ( )[ τ τ ] = + ( )[ q ( ) H/( ) q( α H ( ) H/) )] e We eque τ o τ o obin he demrcion curve in which he disribuion of preferences in he workers populion remins consn over ime which, s i cn be observed, depends on. This equion is ( ) =. This epression is decresing α wih. Anoher usul w of epressing his demrcion curve is o wrie & ( ) = 0. Given priculr vlue of he preferences disribuion in he emploers > e > populion, if ( ) hen nd > 0. < < < Now we proceed o nlze he socilizion decision of he emploers prens. We relege gin he deiled clculions of he levels of culurl inolernce nd he opiml educion effor funcions o he Appendi. The dnmics for he emploers disribuion of preferences is given b: + e = + ( )[ τ τ ] = H + ( )[ q ( ) q H ( β /) ] If we eque τ e o τ, we obin he demrcion curve in which he disribuion of preferences in he emploers populion remins consn over ime, which s i cn be observed does no depend on. This equion is =. Anoher β w of epressing his demrcion curve is o wrie & = 0. If > < e > hen < nd > 0. < 4

26 Preliminr version o be published s Working Pper b BBVA Foundion In Figure, we represen he phse digrm of his nonliner difference equion ssem in wo vribles. The direcionl rrows indice he ineremporl movemen of nd. The quliive phse digrm nlsis ields h here is sble sed se or node of he dnmicl ssem in he inersecion of boh demrcion curves: b - / = nd =. b To supplemen his phse digrm nlsis we mke in he Appendi locl sbili nlsis of his fied poin. Recll h we hve run his nlsis for regions nd 3 bu he sepring equilibrium is onl epeced nd pled in region 3, becuse of he equilibrium selecion mde he beginning of his secion. Therefore, he sed se (, ) onl eiss if > ˆ. Noice h when ˆ he dnmics will led o region, where he p e equilibrium is pled. This ler siuion is more likel for high vlues of he workers power λ nd resonble vlues, from he eperimenl poin of view, of he prmeer α (he degree of disdvngeous inequi version), nmel, α >. 5

27 Preliminr version o be published s Working Pper b BBVA Foundion 6.3. The dnmics of preferences when gens coordine in he equilibrium In region 4, where nd ³ ˆ, here is relivel high proporion of selfish workers nd sufficienl low proporion of inequi verse emploers nd here p eiss pooling equilibrium e. In his equilibrium boh pes of worker choose o mke specific invesmen (S) nd he selfish emploer offers b = 0 nd he inequi verse emploer offers b = /. Now, s in he previous cse, ll pes of prens hve sricl posiive levels of culurl inolernce nd consequenl, he will hve incenives for cive socilizion. For emple, selfish worker pren epecs h when his child urns ou o be selfish will obin n epeced poff of ( ) H/ nd when his child urns ou o be inequi verse will obin his sme epeced poff from he inequi verse emploers bu, s he will punish selfish emploer, he will incur in n epeced cos of zλ H. This ler moun is he level of culurl inolernce of he selfish pren. Proceeding in he sme w s in he previous secion we relege he deiled clculions of ll he levels of culurl inolernce nd he opiml educion effor funcions o he Appendi. We obin he following dnmics of he disribuion of preferences in he workers' populion: + e = + ( )[ τ τ ] = + ( )[ q zλ H ( ) qλ H ( α z(+ α)) ] e If we eque τ o τ we obin he demrcion curve in which he disribuion of preferences in he workers populion remins consn over ime. This equion is z =, (- z) nd i is independen of. If > e hen < 6 > < p e nd > 0. < We cn ppl he sme procedure o nlze he socilizion decision of he emploers prens (see he Appendi). In his cse we ge he following dnmics of he disribuion of preferences in he emploers' populion.

28 Preliminr version o be published s Working Pper b BBVA Foundion = + (- )[ - ]= e + + (- )[ q[ H/ - (- ) l H]( - )- ( qh [ /- [ ( - b) H+ (- )( H- l H- b( H- l H+ zl H)]] )]. If we eque τ e o τ, we obin he demrcion curve in which he disribuion of preferences in he emploers populion remins consn over ime. This / ( ) λ equion is ( ) =. As i cn be checked his epression is β ( λ ( )( z)) incresing in. Given priculr vlue of he preferences disribuion in he populion of > e > workers, if ( ) hen nd > 0. < < < In Figure 3, we represen he phse digrm of his nonliner difference equion ssem in wo vribles. As we know he direcionl rrows indice he ineremporl movemen of nd. 7

29 Preliminr version o be published s Working Pper b BBVA Foundion The quliive phse digrm nlsis ields h here is sble sed se or node of he dnmicl ssem in he inersecion of boh demrcion curves: z = nd ( - z ) æ (- z) - zö /- l è ç (- z) ø =. æ l ( ( z) z) ö b ç çè ø Once gin he sed se (, ) onl eiss if > ˆ nd <. In he cse h one or boh of hese condiions do no hold, he dnmics will led o region or, lernivel, o region 3 s we will nlze in he ne secion. In he following secion we will use ll he previous dnmic nlsis in order o chrcerize he long run regimes in he lbour mrke. 7. Preferences disribuion nd lbour culures in he long run Our model ields differen long run oucomes, sble sed ses of he culurl dnmics, depending on he priculr vlues of he prmeers of he emplomen relionship. And, in some cses, depending lso on he iniil condiions of he dnmics. The prmeers h deermine he finl resul re hose concerning he blnce of power. Nmel, he workers power ( λ ), h is, he miml shre of he surplus he re ble o desro nd he unir cos of punishing ( z ). Bu i is lso imporn he degree of inequi version of fir-minded workers nd emploers. Wih he ssumpion of low surplus equl o zero ( l = 0 ), he size of he high surplus H (h is, he ne gins from cooperion) does no influence he long run oucome. In his secion we will chrcerize precisel he bsin of rcion of he differen sed ses of he dnmics. 8

30 Preliminr version o be published s Working Pper b BBVA Foundion 7.. An Akerlof-pe equilibrium p Le e sed se denoe n sble sed se of he preferences dnmics p p where he perfec Besin equilibrium e is pled. Noice h in n e sed se he proporion of selfish workers in he populion,, hs o be smller or equl p hn he criicl vlue ˆ. There lws eiss n e sed se in our model, ecep when ˆ equls o zero which occurs when λ = /. An 9 p e sed se is full efficien oucome where reciproci is work. Emploees mke specific invesmen nd emploers reciproce b rewrding heir cooperion wih high fir wges. This is he reson wh we denoe his siuion s n Akerlof-pe or " gif-echnge" lbour culure. Neverheless, here re some differences wih he Akerlof rdiionl model. The firs one is minor difference: in his model emploers rus on workers offering high wges nd hen workers reciproce eering high effor (or mking cosl invesmen). However, in our model he order of moves is reversed. The second nd min difference is h in our emplomen relion he " echnge of gifs" works becuse here is credible hre of he inequi verse workers of hrshl punishing low wges or hold up b he emploers. Ne, in he following se of proposiions we chrcerize he bsin of rcion of his lbour regime. Proposiion An iniil pir of disribuions, ) in Regions nd is n p e sed se. ( 0 0 Recll h Regions nd re defined b he condiion ˆ = ( l - /)/ l. This proposiion mens h for n iniil condiion of he socie where here is significn frcion of inequi verse workers nd independenl of he frcion of selfish emploers, boh pes of emploers se high wges. Selfish emploers prefer o void punishmen given he credible hre of he fir-minded workers. This resul is corollr of he nlsis mde in he previous secion bou regions nd. Noice h he size of hese regions is bigger he higher is λ. In he limi, when λ =, ˆ =/.

31 Preliminr version o be published s Working Pper b BBVA Foundion p Bu he bsin of rcion of he e sed ses includes oher regions for some priculr configurions of he prmeers of he model. Proposiion. Assume h dnmics converges o n The condiion ˆ, hen for n, ) in Region 3 he p e sed se wih = ˆ ( 0 0 nd >. (see Figure 4). ˆ is equivlen o he following resricion on he prmeers ( β 0.5)/ α ( λ 0.5)/ λ. This resricion is more likel o be sisfied for high vlues of he workers power λ nd resonble vlues, from he eperimenl poin of view, of he prmeer α (he degree of disdvngeous inequi version), nmel, α >, s i ws commened in he previous secion. The proof of his proposiion follows from he quliive nlsis of he phse digrm represened in figure 4. Noice h for, ) such h 0 > ˆ nd > 0 ( 0 0 he mrke iniill coordines in he inefficien sepring equilibrium where onl selfish workers mke specific invesmen. Bu for mos of his region 3 he incenives o socilize of inequi verse workers re greer hn hose of selfish workers, h is, > nd decreses over ime unil i evenull reches ˆ. From here on, e everbod epecs nd pls he Akerlof-pe equilibrium. 30

32 Preliminr version o be published s Working Pper b BBVA Foundion Proposiion 3 Assume h ˆ, hen, ) If ˆ, hen for n ( 0, 0) in Region 4 he dnmics converges o n sed se wih = ˆ (see Figure 5). p e b) If ˆ, bu < hen for n, ) in Region 4 he dnmics converges o n p e sed se wih = ˆ ( 0 0 nd >. (see Figure 6). 3

33 Preliminr version o be published s Working Pper b BBVA Foundion Corollr. Under he condiions of Proposiion 3, n Akerlof-pe equilibrium is he unique sble sed se oucome of he dnmics. Th is, for n iniil p condiion in n Region here is convergence o n e sed se nd ˆ. Therefore, proposiion 3 cpures siuion in which he bsin of rcion of he Akerlof-pe equilibrium coincides wih he whole spce of preferences disribuions. The proof of his proposiion follows from he quliive nlsis of he phse digrm represened in figure 5 nd 6. In cse ) (see figure 5), noice h for, ) ( 0 0 in region 4, h is, for preferences disribuion in he populion of workers wih relivel high proporion of selfish individuls nd relivel low proporion of p selfish emploers, gens epec nd pl he equilibrium e. Bu, s < ˆ, hen for ll workers preferences disribuion he incenives o socilize of inequi verse e workers re greer hn hose of selfish workers, h is, > nd decreses over ime unil evenull i reches ˆ. Finll, in cse b), when > ˆ, bu > (Figure 6), wh essenill hppens is h if he dnmics srs wih high proporion of selfish workers nd low proporion of selfish emploers (region 4) hen he socilizion effor of he ler re greer hn he effor of inequi verse emploers. Therefore, increses unil region 3 is reched, where he sepring equilibrium is pled nd he socilizion effor of inequi verse workers is greer hn h of selfish workers. Evenull he p dnmics converges o siuion where > bu > ˆ. This is e sed se. Noice h in he wo previous proposiions he condiion ˆ holds. This implies, s i hs been lred menioned, high vlue of he workers power λ. However, lso for some siuions in which he blnce of power is no so high ( λ smll), he bsin of rcion of he e P sed se cn be greer hn regions nd. Proposiion 4 Assume h 4 he dnmics converges o n > ˆ, bu < ˆ, hen for n, ) in Region p e sed se wih ˆ ( 0 0 = (see Figure 7). 3