Rationality and Equilibrium: A Symposium in Honor of Marcel K. Richter PDF
Preview Rationality and Equilibrium: A Symposium in Honor of Marcel K. Richter
Studies in Economic Theory Editors Charalambos D.Aliprantis Purdue University Department ofEconomics West Lafayette,in47907-2076 USA Nicholas C.Yannelis University ofIllinois Department ofEconomics Champaign,il61820 USA Titles in the Series M.A.Khanand N.C.Yannelis(Eds.) N.Schofield Equilibrium Theory Mathematical Methods in Economics in Infinite Dimensional Spaces and Social Choice C.D.Aliprantis,K.C.Border C.D.Aliprantis,K.J.Arrow,P.Hammond, and W.A.J.Luxemburg(Eds.) F.Kubler,H.-M.Wuand N.C.Yannelis(Eds.) Positive Operators,Riesz Spaces, Assets,Beliefs,and Equilibria and Economics in Economic Dynamics D.G.Saari D.Glycopantis andN.C.Yannelis(Eds.) Geometry ofVoting Differential Information Economies C.D.Aliprantisand K.C.Border A.Citanna,J.Donaldson,H.M.Polemarchakis, Infinite Dimensional Analysis P.Siconolfiand S.E.Spear(Eds.) Essays in Dynamic J.-P.Aubin General Equilibrium Theory Dynamic Economic Theory M.Kaneko M.Kurz(Ed.) Game Theory and Mutual Misunderstanding Endogenous Economic Fluctuations S.Basov J.-F.Laslier Multidimensional Screening Tournament Solutions and Majority Voting V.Pasetta A.Alkan,C.D.Aliprantisand N.C.Yannelis Modeling Foundations ofEconomic Property (Eds.) Rights Theory Theory and Applications G.Camera(Ed.) J.C.Moore Recent Developments on Money and Finance Mathematical Methods for Economic Theory 1 C.Schultzand K.Vind(Eds.) Institutions,Equilibria and Efficiency J.C.Moore Mathematical Methods C.D.Aliprantis,R.L.Matzkin, for Economic Theory 2 D.L.McFadden,J.C.Moore and N.C.Yannelis(Eds.) M.Majumdar,T.Mitraand K.Nishimura Rationality and Equilibrium Optimization and Chaos K.K.Sieberg Criminal Dilemmas M.Florenzanoand C.Le Van Finite Dimensional Convexity and Optimization K.Vind Independence,Additivity,Uncertainty T.Casonand C.Noussair(Eds.) Advances in Experimental Markets F.Aleskerovand B.Monjardet Utility Maximization.Choice and Preference Charalambos D.Aliprantis Rosa L. Matzkin · Daniel L. McFadden James C. Moore · Nicholas C.Yannelis Editors Rationality and Equilibrium A Symposium in Honor of Marcel K.Richter With 8 Figures and 3 Tables 123 Prof.Charalambos D.Aliprantis Prof.James C.Moore Purdue University Purdue University Krannert School ofManagement Krannert School ofManagement Department ofEconomics Department ofEconomics West Lafayette,IN 47907-2076 West Lafayette,IN 47907 USA USA E-mail:[email protected] E-mail:[email protected] Prof.Rosa L.Matzkin Prof.Nicholas C.Yannelis Northwestern University University ofIllinois Department ofEconomics Department ofEconomics Evanston,IL 60208 Champaign,IL 61820 USA USA E-mail:[email protected] E-mail:[email protected] Prof.Daniel L.McFadden University ofCalifornia Department ofEconomics Berkeley,CA 94720-3880 USA E-mail:[email protected] Cataloging-in-Publication Data Library ofCongress Control Number:2005937894 ISBN-10 3-540-29577-1 Springer Berlin Heidelberg New York ISBN-13 978-3-540-29577-8 Springer Berlin Heidelberg New York This work is subject to copyright.All rights are reserved,whether the whole or part of the material is concerned,specifically the rights of translation,reprinting,reuse of illustrations,recitation,broadcasting,reproduction on microfilm or in any other way, and storage in data banks.Duplication ofthis publication or parts thereofis permitted only under the provisions ofthe German Copyright Law ofSeptember 9,1965,in its current version,and permission for use must always be obtained from Springer-Verlag. Violations are liable for prosecution under the German Copyright Law. Springer is a part ofSpringer Science+Business Media springeronline.com © Springer-Verlag Berlin Heidelberg 2006 Printed in Germany The use ofgeneral descriptive names,registered names,trademarks,etc.in this publi- cation does not imply,even in the absence ofa specific statement,that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Cover design:Erich Kirchner Production:Helmut Petri Printing:Strauss Offsetdruck SPIN 11572275 Printed on acid-free paper – 42/3153 – 5 4 3 2 1 0 Foreword to ‘Rationality and Equilibrium’ – A Symposium in honor of Marcel K. Richter CharalambosD.Aliprantis1,RosaL.Matzkin2,DanielMcFadden3, JamesC.Moore1,andNicholasC.Yannelis4 1 DepartmentofEconomics,PurdueUniversity,WestLafayette,IN47907,USA (e-mail:[email protected];[email protected]) 2 DepartmentofEconomics,NorthwesternUniversity,Evanston,IL60208,USA (e-mail:[email protected]) 3 DepartmentofEconomics,UniversityofCalifornia,Berkeley,CA94720-3880,USA (e-mail:[email protected]) 4 DepartmentofEconomics,UniversityofIllinoisatUrbana-Champaign,IL61820,USA (e-mail:[email protected]) This collection of papers is dedicated to Marcel K. Richter, in appreciation of the fundamental impact that his research, mentoring, and personality has had on economicsandoneconomists. MarcelK.Richter’sresearchhastakeneconomictheorytoplacesitneededto go,andalongthewayhaslefttight,crisp,important,andbeautifullyelegantresults. Eachpaperisadestination,aresultthatisworththetrip,astopthatinstructsthe studentontheeffectivenessofmathematicsandtheliberatingpowerofcrystalline logic.Nopaperofhisiscarelesslywritten. A good representative of Ket Richter’s work is his 1966 Econometrica paper “RevealedPreferenceTheory.”Thispaperhashadaprofoundinfluence,notonlyon theproblemofpreferencecharacterization,butalsoontheuseofpowerfullogical tools in economic theory. Using set theory and mathematical logic, it provided a simple,clear,andgeneralmethodtoaddressthetopicofconsumerrationality,which stronglycontrastedwiththecomplexalternativeliteratureonrevealedpreference andintegrabilitytheory.Thiswasfollowedby“RationalChoice”andbythejoint work with Leonid Hurwicz, “Revealed Preference Without Demand Continuity Assumptions,” both published in Preferences, Utility and Demand, edited by J. Chipman,L.Hurwicz,M.K.Richter,andH.Sonnenschein(1971). Many other topics in economic theory benefited from Ket Richter’s lucidity. Hedevelopedfundamentalrelationshipsbetweenpreference,utilityanddemand, in,amongothers,“ContinuousandSemicontinuousUtility”(IER1980),“Duality andRationality”(JET1979),“AnIntegrabilityConditionwithApplicationstoUtil- ityTheoryandThermodynamics”(withLeonidHurwicz,JME1979),and“Ville AxiomsandConsumerTheory”(withLeonidHurwicz,Econometrica1979).To- gether with G. Fuhrken, he wrote “Polynomial Utility” (ET 1991) and “Additive Utility”(ET1991).WithTaesungKimhewrote“NontransitiveNontotalConsumer Theory”(JET1986).WithRosaL.Matzkin,heprovidedconditionsforrational- ization of finite demand observations, in “Testing Strictly Concave Rationality” (JET,1991),andwithKamChauWong,heprovidedconditionsfortheexistence of a concave utility function on finite sets, in “Concave Utility on Finite Sets” VI Aliprantisetal. (JET2004).His“CardinalUtility,PortfolioSelectionandTaxation”(RES1960) developedthetheoryofportfoliodemandundertheassumptionthattheutilityof theinvestordependedonlyoncharacteristicsoftheprobabilitydistributionofthe portfolio’suncertainearnings. ThetheoryofthecoreandWalrasianallocationsbenefitedfromKetRichter’s major contributions, such as “Existence of Nonatomic CoreWalrasAllocations” (JET1986)and“TheCore-WalrasEquivalence”(JET1984),bothco-authoredwith ThomasArmstrong,andfrom“Coalitions,CoreandCompetition”(JET1971).In “InvarianceAxiomsandEconomicIndexes”(Econometrica1966),hecontributed to the axiomatic foundations of index number theory.With Leonid Hurwicz, Ket generalizedconstrainedmaximizationandimplicitfunctiontheoryin“Optimiza- tion and Lagrange Multipliers” and in “Implicit Functions and Diffeomorphisms withoutC1”(bothpublishedinAdvancesinMathematicalEconomics2003). Morerecently,withKamChauWong,KetRichterhasmovedforwardthetheory ofboundedrationality,bystudyingissuesinvolvingthecomputabilityanddefin- ability of utility, demand, and equilibrium. Some of the papers in this series are “Computable Preference and Utility” (JME 1999), “Noncomputability of Com- petitiveEquilibrium”(ET1999),and“DefinableUtilityinO-MinimalStructures” (JME2000). Revealed preference is, however, the topic with which Marcel K. Richter is mostassociated.Besidesthepapersmentionedaboveonthistopic,otherclassics arehispaperwithLeonardShapiro,“RevelationsofaGambler”(JME1978);his well known paper with Daniel McFadden, “Stochastic Rationality and Revealed Stochastic Preference” (in Preference, Uncertainty and Rationality, edited by J. Chipman, D. McFadden, and M.K. Richter, 1990), which laid the foundation for theexistenceofarandomutilityrationalizationofprobabilisticchoice;andhisjoint paperwithAndreuMasColell,RolfMantel,andDanielMcFadden,“ACharacter- izationofCommunityExcessDemandFunctions”(JET1974),inwhichrevealed preference theory was used to demonstrate that a variant of the Sonnenschein- Debreu characterization held without the added restriction to a strictly positive closedpricecone. Marcel K. Richter’s mentoring has been as unique as his research.The input and dedication he has demonstrated in his research has paralleled the input and dedicationhehasgiventohisstudents.ForKetRichter,nostudentthesisisready to be defended until all ideas are clearly presented, all details are worked out, and all the lines of the thesis have undergone the close scrutiny of his red pen. Infact,KetRichterhasbeenaconsummatementor.AllUniversityofMinnesota studentsineconomicshavebenefitedfromKet’sfriendlyhelpandopendoor,and hiswillingnesstotakeupanytopic.Ket’spersonalityisasimpressiveas,andvery muchinlinewith,hisresearch.Hetrulycaresabouteachpersonandmakeshisor herhappinesshisownconcern. The papers assembled in this issue are by colleagues, students, and admirers of Marcel K. Richter. They deal with topics deeply connected to his work and interests,suchaspreferences,demand,equilibrium,coreallocations,andtestable restrictions. On behalf of everybody who has contributed to this symposium, we wishKetallthebestandthankhimforhismanycontributions. Table of Contents Forewordto“RationalityandEquilibrium–ASymposiuminHonorof MarcelK.Richter” CharalambosD.Aliprantis,RosaL.Matzkin,DanielL.McFadden, JamesC.Moore,NicholasC.Yannelis............................... V Revealedstochasticpreference:asynthesis DanielL.McFadden ............................................. 1 Communicationindynasticrepeatedgames: “whitewashes”and“coverups” LucaAnderliniandRogerLagunoff ................................. 21 ThestructureoftheNashequilibriumsetsofstandard2-playergames LinZhou ...................................................... 57 Nashequilibriumingameswithincompletepreferences SophieBade ................................................... 67 Remarksconcerningconcaveutilityfunctionsonfinitesets YakarKannai................................................... 91 Walrasianversusquasi-competitiveequilibriumandthecore ofaproductioneconomy JamesC.Moore ................................................ 103 CharacterizationandincentivecompatibilityofWalrasianexpectations equilibriumininfinitedimensionalcommodityspaces CarlosHerve´s-Beloso,EmmaMoreno-Garc´ıa,NicholasC.Yannelis ....... 119 Comparativestaticsandlawsofscarcityforgames AlexanderKovalenkovandMyrnaWooders........................... 141 Existenceofequilibriaforeconomieswithexternalitiesandameasure spaceofconsumers BernardCornetandMihaelaTopuzu ................................ 169 Identificationofconsumers’preferenceswhentheirchoices areunobservable RosaL.Matzkin ................................................ 195 VIII TableofContents Log-concaveprobabilityanditsapplications MarcBagnoliandTedBergstrom................................... 217 Notesonstochasticchoice AndreuMas-Colell .............................................. 243 Revealed stochastic preference: (cid:1) a synthesis DanielL.McFadden DepartmentofEconomics,UniversityofCalifornia,Berkeley,CA94720-3880,USA (e-mail:[email protected]) Received:March13,2003;revisedversion:February11,2004 Summary. Theproblemofrevealedstochasticpreferenceiswhetherprobability distributionsofobservedchoicesinapopulationforvariouschoicesituationsare consistentwithahypothesisofmaximizationofpreferencepreordersbymembers ofthepopulation.Thisisapopulationanalogoftheclassicalrevealedpreference problemineconomicconsumertheory.Thispapersynthesizesthesolutionstothis problemthathavebeenobtainedbyMarcelK.Richterandtheauthor,andbyJ.C. Falmagne,inthecaseoffinitesetsofalternatives,andutilizesunpublishedresearch ofRichterandtheauthortogiveresultsforthenon-finitechoicesetsencountered ineconomicconsumertheory. Keywords and Phrases: Choice, Stochastic preference, Revealed preference, Randomutilitymaximization. JELClassificationNumbers: D1,C6. 1 Introduction The problem of revealed stochastic preference asks the question:Are the distri- butionsofchoicesobservedforapopulationofindividualsinavarietyofchoice situations consistent with rational choice theory, which postulates that individu- alsmaximizepreferences?Ineconomicconsumertheory,eachchoicesituationis defined by a budget set; in psychometrics, by the alternatives offered in an ex- periment;andinpoliticalvotingbehavior,bytheissuespresentedinanelection. (cid:1) ThepreparationofthispaperwassupportedbytheE.MorrisCoxendowmentattheUniversityof California,Berkeley.IamindebtedtoRobertAnderson,SalvadorBarbara,WernerHildenbrand,Rosa L.Matzkin,andAvivNevoforusefulsuggestionsandcomments.IamespeciallyindebtedtoMarcel K.Richter,whowasthesourceofmanyoftheideasandargumentscontainedinthispaper.
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