公平与效率外文文献翻译中英文.docx

公平与效率外文文献翻译中英文.docx

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公平与效率外文文献翻译中英文

公平和效率中英文2019

英文

Fairshareandsocialefficiency:

Amechanisminwhichpeersdecideonthepayoffdivision

RodFalvey，ShravanLuckraz

Abstract

Weproposeandexperimentallytestamechanismforaclassofprincipal-agentproblemsinwhichagentscanobserveeachothers'efforts.Inthismechanismeachplayercostlesslyassignsashareofthepietoeachoftheotherplayers,afterobservingtheircontributions,andthefinaldistributionisdeterminedbytheseassignments.Weshowthatefficiencycanbeachievedunderthissimplemechanismand,inacontrolledlaboratoryexperiment,wefindthatplayersrewardothersbasedonrelativecontributionsinmostcasesandthattheplayers'contributionsimprovesubstantiallyandalmostimmediatelywith80percentofplayerscontributingfully.

Keywords：

Experimentaleconomics，Fairness，Mechanismdesign

Itcanbedifficultforaprincipaltoobserveindividualagent'seffortlevels,particularlywhenagentsworkinteams.Theextensivemonitoringthatwouldberequiredmaynotbefeasibleorcost-effective.Profitsharinghasbeensuggestedasaresponse（WeitzmanandKruse,1990）,sincegivingeachoftheagentsastakeinanenterprise'sprofitsdoesprovidealinkbetweenagentcontributionandagentrewardthatismissingfromafixedwageorsalarystructure.Butunderanequalsharingallocation,whichisthenaturalallocationforaprincipaltoimposewhenshecannotobserveindividualagent'sbehaviour,a free-riderproblem arisessinceeachagentbearsthefullcostoftheircontributionbutonlyreaps 1Nthofthebenefitinan N-agentteam.Unlessthecostsofcontributionarelowortheinterdependenciesbetweenagentproductivitiesinteamproductionarehigh（HeywoodandJirjahn,2009）,agentswillnotcontributetheirsocialoptimalcontributionunderanequal-sharingregime.Ifrewardsarenotrelatedtocontribution,anagentwhofeelsunder-compensatedmayendupreducinghercontribution.

Althoughtheprincipalmaybeunabletoobserveagents'contributions,therewillbeoccasionswheretheagentsthemselvesareinapositiontoobserveeachothers'actions.1 Thechallengethenfortheprincipalistodesignamechanismthatelicitsandusesthisinformationtoinducetheappropriatelevelsofcontributionfromtheagents.Inthiscontext,weconsiderasimplemechanisminwhichagentsarenotonlyabletomonitoreachother,butalsoinpositionstodetermineeachother'spayoffs.Themechanismweproposetakestheformofatwo-stagegame.Inthefirststage,eachplayerchoosessomecontributionlevelandinthesecondstage,afterhavingobservedeachothers'contributions,eachplayerproposesafractionofthetotalsurplustobereceivedbyeachoftheremainingplayers.Aplayer'sfinalsharedependsontheotherplayers'allocationtowardher.

Welabelourmechanismthe“GalbraithMechanism”（GMhereafter）astheideaisinspiredbyJohnKennethGalbraithwho,inanasidein TheGreatCrash1929,describedabonussharingschemeusedbytheNationalCityBank（nowCitibank）intheU.S.inthe1920s.Underthisschemeeachofficerwouldsignaballotgivinganestimatedshareofthebonuspooltowardseachoftheothereligibleofficers,himself/herselfexcluded.Theaverageoftheseshareswouldthenguidethefinalallocationofthebonustoeachoftheofficers（Galbraith,1963,p.171）.Thissharingmechanismcanbeappliedtomanyeconomicproblemsincludinggameswithpositiveexternalitiesandprincipal-agentproblemsinwhichtheprincipalneedstodistributesomecommonresourceamongsttheagents.

ThecrucialfeatureoftheGMisthathowaplayerallocatessharesinthesecondstagedoesnotaffectherownpayoff.Therefore,playersareabletorewardorpunishtheirpeersbasedonthefirststageobservedactions.Anumberofstudieshavedemonstratedthatplayersexhibit socialpreferences to“punish”thosewhofree-rideonthegroupproduction（FehrandGächter,2000）andto“reward”thosewhocontributemorethanthegroupaverage（Seftonetal.,2007 ;NosenzoandSefton, 2012 ）.Whilesuchsocialpreferencesmovetheoutcometowardssocialefficiency, self-interest tendstorestricttheirapplicationandthesocialcoststhatthesepunishmentsandrewardsimposeonallpartiesinvolvedtendtolimittheirultimatesuccess（see Chaudhuri（2010） forareview）.3 TheGMisbasedonanendogenouspayoffallocationinwhichplayerscanfreelydecideonsomefractionoftheco-players'payoffs.Playersarefreetopunish,toreward,toallocateequallyoreventoallocaterandomlytotheremainingplayers,whilenocostsareincurredbyanyplayersintheallocationexercise.

Thedownsideofallowingplayersthefreedomtorewardandpunishinthiswayisapotentialformultiplicityof NashEquilibria atthesecondstageoftheGMgame.Withoutmorestructure,everyallocationisaNashEquilibriuminthesecondstage.Onemethodofremovingtheresultingarbitrarinessisbyexplicitlyincorporatingabehaviouralcomponentintothepayofffunction,whichcouldbeseenasreflectingtheplayer'ssubjectivenotionofa“fair”allocation.4 Butratherthanimposingasolutioninthisway,weleavethequestionofhowtheplayersactuallyallocatetobeuncoveredintheexperimentsthatfollow.Thatsaid,ourinvestigationofequilibriainthiscontributiongamedoesrevealalinkbetweenefficiencyand“fairness”.Muchofthetheoreticalliteratureonfairnessfocusesonequalityandequalshare（e.g., FehrandSchmidt,1999 ）regardlessofcontributions.Butagrowingempiricalliteratureappealstootherfairnesscriteriatojustifyunequalallocations,e.g., Adams（1965）; Konow （1996; 2000; 2009）; GächterandRiedl（2006）; Cappelenetal.（2007）; Shaw（2013）; Cappelenetal.（2013）.5 Prominenthereisthenotionofdistributivejusticefirstexploredbysociologists（Homans,1958; Adams,1965）andlateradoptedbybehaviouraleconomists（Selten,1978 ）.

Distributivejusticeisoftendefinedbytheprinciplethataplayer'sentitlementtowardssomegroupoutcomeshouldbeproportionaltohercontributiontothatoutcome.6 Inthenextsection,weestablishthatsuch“fair”allocationbehaviourcansupportefficiency（fullcontributions）aspartofaSPNEofthiscontributiongame,forallpositivereturnstototalcontributions.Itisapivotalcaseinthatothermorepro-contributionbiasedallocations（i.e.allocationsthatgivedisproportionatelylargerallocationsharestothosewithhighercontributionshares）alsosupporttheefficientequilibriumunderthesameconditions,butanti-contributionbiasedallocations（i.e.allocationsthatgivedisproportionatelylargerallocationsharestothosewithlowercontributionshares）,suchasequalshares,onlysupporttheefficientequilibriumathigherreturnstototalcontributions.Proportionalallocationsfeatureprominentlyinourexperimentalresults.

TheGMisalso“simpler”thanotherendogenousmechanismsproposedtosolvesocialdilemmaproblems.Forexample, AndreoniandVarian（1999） studiedamechanismwhereplayerscanagreeonapre-playcontractbeforeplayingthe prisoner'sdilemma game.However,theirmechanismdoesnotperformwellwhentestedinlaboratorysettings（Hamaguchietal.,2003; Brachtetal.,2008）.Whilethereareothermechanismsthatperformbetterinthelaboratory,forexample, Falkingeretal.（2000）; Masudaetal.（2014） and Stoddardetal.（2014）,theyeitheraddanenforcementinstitution,or“impose”aninformedthirdpartytoallocatetheshares.Inthecontextofanuninformedprincipalandinformedagents,theGMisamethodofdetermininganinformedallocationfortheprincipaltomakewhichrequiresonlythattheprincipalcollatetheallocationsharesproposedbytheplayersanddistributeaccordingly.7 Providedtheplayersareinclinedtorewardcontributioninthesecondstage,andtheyanticipatethishappeningatthefirststage,theGMshouldyieldoutcomesclosertosocialefficiencythananequalsharesmechanism.8

Perhapsthemodelclosesttooursis Baranski（2016） whoconsidersaclassofvoluntarycontributionmechanisminwhichtheplayers'sharesofthegroupfundaredeterminedusinga BaronandFerejohn（1989） multilateralbargainingprocedureinwhicheachplayercanberandomlychosentobeaproposeratacertainperiod.Ineachperiod,afteradivisionisproposed,theremainingplayerscanvotetoagreeordisagreewiththeproposal.Thebargainingprocessendsifamajorityagreewiththeproposerandthefundisdividedaspertheproposal.ThemostimportantdistinctionbetweenthismechanismandtheGMliesintheallocationstagewhichtakestheformofaone-shotgameintheGM,whereasinBaranski'smechanism,itisgivenbyamulti-stagebargainingprocess.Furthermore,theGMdoesnotrequirearandomlychosenproposeraseachplayersimplyproposesashareforhispeers.Intermsofexperimentresults,bothmechanismsenjoyasubstantialincreaseinthecontributionlevelsoncetheyareintroduced.9

Insummary,themaincontributionofthispaperistoproposeasimplemechanismandtotestitexperimentally.Asnoted,thismechanism:

（i）allowscostlessrewardandpunishmentattheallocationstage;（ii）removesthebiasarisingwhenaplayerproposesanallocationtohimself;and（iii）avoidsthenecessityofimposinganinformedallocatororrandomlyselectingoneaspartofabargainingprocess.Onlylowreturnstoscale,whereequalshareswouldnotautomaticallygeneratefullcontributions,areconsidered.Providedplayersrewardothersbasedontheircontributionsattheallocationstage,andanticipatesuchrewardsatthecontributionstage,weexpectthatsocialefficiencycanbeachievedunderthismechanism.Thisallocativebehaviourdoesseemtobeprevalentin