搜索
EquilibriumintheJungle∗MichelePiccioneDepartmentofEconomicsLondonSchoolofEconomicsandArielRubinsteinSchoolofEconomics,TelAvivUniversityandDepartmentofEconomics,NewYorkUniversityfinethenotionofjungleequilibriumanddemonstratethatanumberofstandardresultsofcompetitivemar-ketsholdinthejungle.JELClassification:C7,D4,S477,B201Keywords:power,involuntaryexchange,jungleequilibrium,com-petitiveequilibrium∗WewishtothankLucaAnderlini,SamuelBowles,LeonardoFelli,PieroGottardi,HeraklisPolemarchakis,AndreaPrat,TayfunSomnez,andRaniSpieglerfortheircom-ments.11IntroductionInthetypicalanalysisofanexchangeeconomy,agentsareinvolvedincon-sumptionandexchangegoodsvoluntarilywhenmutuallybeneficial.Theendowmentsandthepreferencesaretheprimitivesofthemodel.Thedistri-butionofconsumptioninsocietyisdeterminedendogenouslythroughtrade.Thispaperismotivatedbyacomplementaryperspectiveonhumanin-teraction.Throughoutthehistoryofmankind,ithasbeenquitecommon(andwesuspectthatitwillremainsointhefuture)thateconomicagents,individuallyorcollectively,usepowertoseizecontrolofassetsheldbyoth-ers.Powerrelationships,eitherformalorinformal,arepervasiveineverysocietyandtakeseveralforms.Often,powerispurelyphysical.Sometimes,however,powerismoregentle.Inthemale-female“market”,forexample,charmandattractionplayakeyroleinobtainingafavoritemate.Inanofficeparkinglot,socialconventionssuchasseniorityallowcontrolofthepreferredparkingplaces.Thepowerofpersuasionenablessometoconvinceotherstotakeactionsagainsttheirowninterest.Weintroduceandanalyzeanelementarymodelofasociety,calledthejungle,inwhicheconomictransactionsaregovernedbycoercion.Thejungleconsistsofasetofindividuals,eachhavingexogenouspreferencesoverbun-dlesofgoodsandexogenous“strength”.Therankingofagentsaccordingtostrengthisunambiguousandknowntoall.Power,inourmodel,hasasimpleandstrictmeaning:astrongeragentisabletotakeresourcesfromaweakeragent.Theframeworkmirrorsabasicexchangeeconomy.Thetotalendowmentofgoodsisexogenous.Thedistributionofpowerinthejungleisthecounter-partofthedistributionofendowmentsinthemarketandisalsoexogenous.Astheincentivestoproduceorcollectthegoodsareignoredinanexchangeeconomy,soaretheincentivestobuildstrengthinthejungle.Wedefineajungleequilibriumasafeasibleallocationofgoodssuchthatnoagentwouldlikeandisabletotakegoodsheldbyaweakeragent.Wedemonstrateseveralpropertiesthattheallocationruleofthejungleshareswiththeallocationruleofanexchangeeconomy.Inparticular,wewillshowthatunderstandardassumptionsajungleequilibriumexists,isParetoeffi-cientandthereexistpricesthat“almost”supportthejungleequilibriumasacompetitiveequilibrium.Theobservationthatmainstreameconomicmodelsignoreavarietyofhu-manactivitiesthatinvolvepowerandthatarerelevanttotheproductionand2distributionofwealthisnotnew.EconomistssuchasSamBowles,HerbertGintis,JackHirshleifer,andHerschelGrossmanhaveemphasizedthispointforlongtime.Herearesomeexamples.Hirshleifer(1994),forexample,saysthat“...themainlineMarshalliantraditionhasneverthelessalmostentirelyoverlookedwhatIwillcallthedarksideoftheforce-towit,crime,war,andpolitics”and“Appropriating,grabbing,confiscatingwhatyouwant-and,ontheflipside,defending,protecting,sequesteringwhatyoualreadyhave-that’seconomicactivitytoo”.Grossman(1995)developsamodelwhereagentsdecidehowmuchefforttoputinproductionandhowmuchtoembedin“extralegalappropriativeactivities”andstudiesitsequilibrium.BowlesandGintis(1992)emphasizethat“powerisbasedonthecapacityofsomeagentstoinfluencethebehaviorofotherstotheiradvantagethroughthethreatofimposingsanction”andanalyzedmarkets,especiallylabormarkets,wherethetermsoftransactionsaredeterminedthroughanonWalrasianprocesswhereanagent’swealthaffectshispower.Theseauthorshavearguedfortheimportanceofinvoluntaryexchangeintheeconomyanditsinclusioninstandardeconomictheory.Incontrast,ourmaingoalistoconstructaformalmodelofinvoluntaryexchangethatissimilartotheWalrasianmodelandyieldscomparableproperties.2TheJungleInthissection,weintroduceasimplemodelinwhichresourcesbecomeavail-ablefordistributionamongagroupofagents.Powerandcoerciongovernstheallocationoftheseresources.Eachoftheagentshasexogenousprefer-encesoverbundlesofgoods.Agentsarerankedaccordingtotheirstrength.Thisrankingisunambiguousandknowntoall.Astrongeragentisabletotakeresourcesfromaweakeragent.Wepresentandstudyanequilibriumconceptthatwecallthejungleequilibriumandinvestigateitsproperties.Weconsideramodelwithcommoditieslabeled1,...,K,andasetofagents,I={1,...,N}.Anaggregatebundlew=(w1,...,wK)0isavail-ablefordistributionamongtheagents.Eachagentiischaracterizedbyapreferencerelation%ionthesetofbundlesRK+andbyaconsumptionsetXi⊆RK+.Thepreferencesofeachagentsatisfythestandardassumptionsofstrongmonotonicityandcontinuity.TheinterpretationofXiisthatagentihasboundsonhisabilitytoconsume.WeassumethatXiiscompactand3convex,andsatisfiesfreedisposal,thatis,xi∈Xi,y∈RK+andy≤xiim-pliesthaty∈Xi.Thedistribu