Selected Title s i n Thi s Serie s

23 Myrn a H . Wooders , Editor , Topic s i n mathematical economic s an d gam e theory Essay s in hono r o f Robert J . Aumann , 199 9 22 Graciel a Chichilnisky , Editor , Topolog y an d markets , 199 9 21 Shigu i Ruan , Gai l S . K . Wolkowicz , an d Jianhon g Wu , Editors , Differentia l equations wit h application s t o biology , 199 8 20 Pete r A . Fillmor e an d Jame s A . Mingo , Editors , Operato r algebra s an d thei r applications II , 199 8 19 Willia m G . Dwyer , Stephe n Halperin , Richar d Kane , Stanle y O . Kochman , Mark E . Mahowald , an d Pau l S . Selic k (Editor-in-Chief) , Editors , Stabl e an d unstable homotopy , 199 8 18 Pano s M . Pardalo s an d Henr y Wolkowicz , Editors , Topic s i n semidefinit e an d interior-point methods , 199 8 17 Joachi m J . R . Cunt z an d Masou d Khalkhali , Editors , Cycli c cohomolog y an d noncommutative geometry , 199 7 16 Victo r P . Snaith , Editor , Algebrai c K-theory , 199 7 15 Stephe n P . Braham , Jac k D . Gegenberg , an d Rober t J . McKellar , Editors , Sixt h Canadian Conferenc e o n genera l relativit y an d relativisti c astrophysics , 199 7 14 Moura d E . H . Ismail , Davi d R . Masson , an d Miza n Rahman , Editors , Specia l functions, g-serie s an d relate d topics , 199 7 13 Pete r A . Fillmor e an d Jame s A . Mingo , Editors , Operato r algebra s an d thei r applications, 199 7 12 Dan-Virgi l Voiculescu , Editor , Fre e probability theory , 199 7 11 Collee n D . Cutle r an d Danie l T . Kaplan , Editors , Nonlinea r dynamic s an d tim e series: Buildin g a bridg e betwee n th e natura l an d Statistica l sciences , 199 7 10 Jerrol d E . Marsden , Georg e W . Patrick , an d Willia m F . Shadwick , Editors , Integration algorithm s an d classica l mechanics , 199 6 9 W . H . Kliemann , W . F . Langford , an d N . S . Namachchivaya , Editors , Nonlinea r dynamics an d stochasti c mechanics , 199 6 8 Larr y M . Bate s an d Davi d L . Rod , Editors , Conservativ e System s an d quantu m chaos, 199 6 7 Willia m F . Shadwick , Perinkula m Sambamurth y Krishnaprasad , an d Tudo r Stefan Ratiu , Editors , Mechanic s day , 199 6 6 Ann a T . Lawnicza k an d Raymon d Kapral , Editors , Patter n formatio n an d lattic e gas automata, 199 6 5 Joh n Chadam , Marti n Golubitsky , Willia m Langford , an d Bria n Wetton , Editors, Patter n formation : Symmetr y method s an d applications , 199 6 4 Willia m F . Langfor d an d Wayn e Nagata , Editors , Norma l form s an d homoclini c chaos, 199 5 3 Anthon y Bloch , Editor , Hamiltonia n an d gradien t flows, algorithm s an d control , 199 4 2 K . A . Morris , Editor , Contro l o f flexible structures , 199 3 1 Michae l J . Enos , Editor , Dynamic s an d contro l o f mechanical Systems : The fallin g ca t and relate d problems , 199 3 This page intentionally left blank http://dx.doi.org/10.1090/fic/023

FIELDS INSTITUT E COMMUNICATIONS

THE FIELD S INSTITUT E FO R RESEARC H I N MATHEMATICA L SCIENCE S

Topics i n Mathematical Economic s and Gam e Theor y Essays i n Honor o f Robert J. Auman n

Myrna H . Wooder s Editor

American Mathematical Societ y Providence, Rhod e Islan d The Field s Institut e for Researc h i n Mathematical Science s

The Field s Institute i s named i n honour o f the Canadia n mathematicia n Joh n Charle s Fields (1863-1932) . Field s wa s a visionar y wh o receive d man y honour s fo r hi s scientifi c work, including election to the Royal Society o f Canada i n 190 9 and to the Royal Society of London i n 1913 . Amon g othe r accomplishment s i n the Servic e o f the internationa l math - ematics Community , Field s wa s responsibl e fo r establishin g th e world' s mos t prestigiou s prize fo r mathematic s research—th e Field s Medal . The Fields Institute fo r Researc h i n Mathematical Science s i s supported b y grants fro m the Ontario Ministry o f Education an d Training and the Natural Science s and Engineerin g Research Counci l o f Canada . Th e Institut e i s sponsore d b y McMaste r University , th e University o f Toronto, th e Universit y o f Waterloo, an d Yor k Universit y an d ha s affiliate d universities i n Ontari o an d acros s Canada .

2000 Subject Classification. Primar y 91Axx , 91Bxx .

Library o f Congress Cataloging-in-Publicatio n Dat a Topics i n mathematica l economic s an d game theor y : essa y i n hono r o f Rober t J . Auman n / Myrna H . Wooders, editor . p. cm . — (Fields Institut e Communications , ISS N 1069-526 5 ; v. 23) Includes bibliographica l references . ISBN 0-8218-0525- 8 (alk . paper) 1. . 2 . , Mathematical . I . Aumann, Rober t J . II . Wooders, Myrn a Holtz. III . Series. QA269.T67 199 9 519.3—dc21 99-04651 3 CIP

Copying an d reprinting. Materia l i n this boo k ma y be reproduced b y any means fo r edu- cational an d scientific purpose s withou t fe e or permission wit h th e exception o f reproduction b y Services that collec t fee s fo r delivery o f documents an d provided tha t th e customary acknowledg - ment o f the source i s given. Thi s consen t doe s no t extend t o other kind s o f copying fo r genera l distribution, fo r advertising o r promotional purposes , o r fo r resale. Request s fo r permission fo r commercial us e o f materia l shoul d b e addresse d t o th e Assistan t t o th e Publisher , America n Mathematical Society , P . O. Bo x 6248, Providence , Rhod e Islan d 02940-6248 . Request s ca n also be mad e b y e-mail t o [email protected] . Excluded fro m thes e provision s i s material i n articles fo r which the author hold s Copyright . I n such cases , requests fo r permission to use or reprint shoul d be addressed directl y to the author(s). (Copyright ownershi p i s indicated i n the notice i n the lower right-hand corne r o f the first pag e of each article. ) © 199 9 by the American Mathematica l Society . Al l rights reserved . The America n Mathematica l Societ y retain s al l rights except thos e grante d to the United State s Government . Printed i n the United State s o f America. @ Th e paper use d i n this boo k i s acid-free an d falls withi n the guidelines established t o ensure permanenc e an d durability. This publicatio n wa s prepared b y The Fields Institute . Visit th e AMS home pag e at URL : http://www.ams.org / 10 9 8 7 6 5 4 3 2 1 0 4 03 02 01 00 9 9 Contents

Preface vi i

Acceptable Point s i n General Cooperativ e n-Perso n Game s 1

ROBERT J . AUMAN N

Non-cooperative Gam e Theor y

Young Measur e Technique s fo r Existenc e o f Cournot-Nash-Walra s Equilibria 3 1 ERIK J . BALDE R Modeling Fre e Choic e i n Games 4 1

STEVEN J . BRAM S

Cooperative Gam e Theor y

Pairwise-Bargained Consistenc y an d Gam e Theory : The Cas e o f a Two-Side d Fir m 6 5 THEO S . H . DRIESSE N A New Characterization o f Totally Balance d Game s 8 3 JUAN ENRIQU E MARTINEZ-LEGA Z

The Worth o f a Cooperativ e Enterpris e t o Eac h Membe r 8 9 MICHAEL MASCHLE R

Bargaining Betwee n Heterogeneou s Organization s 9 5 GORDON H . MCCORMIC K an d GUILLERM O OWE N

Coalition Structur e Value s o f Mixed Game s 10 5 RICHARD P . MCLEA N

Aumann-Shapley Rando m Orde r Value s o f Non-Atomic Game s 12 1

LAKSHMI K . RAU T

Economics an d Socia l Choic e

On the Existenc e o f Cor e Allocations i n a Large Econom y wit h Incentive-Compatibility Constraint s 13 9 BETH ALLE N VI CONTENTS

Economic Application s o f Probabilistic Chea p Tal k 15 3 BHASKAR CHAKRAVORTI , JOH N P . CONLE Y an d BAR T TAU B

Multilaterally Strategy-Proo f Mechanism s i n Rando m Aumann-Hildenbrand Macroeconomie s 17 1 PETER J . HAMMON D

Arbitrage wit h Price-Dependen t Preferences : Equilibrium an d Marke t Stabilit y 18 9 FRANK H . PAGE , JR . an d MYRN A H . WOODER S

A Smooth Socia l Choic e Method o f Preference Aggregatio n 21 3 NORMAN SCHOFIEL D

Clubs, Nea r Market s an d Marke t Game s 23 3 MARTIN SHUBI K an d MYRN A H . WOODER S

On Economi c Application s o f the Kuhn-Fourie r Theore m 25 7 ARJA H . TURUNEN-RE D an d ALA N D . WOODLAN D

Coalition-Proofness o f the Competitiv e Allocation s i n a n Indivisible Good s Marke t 27 7 JUN WAK O

Appendix: Presentation s a t th e Field s Institute Worksho p New Directions i n the Theor y o f Markets an d Game s 28 5 Preface

Since the publication o f the Theory o f Games by John von Neumann and Oska r Morgenstern, gam e theory has played a continually increasin g role in economics. I t has als o bee n o f growin g importanc e i n othe r sciences , includin g biology , politica l science an d psychology . Severa l scientist s mad e earl y semina l contribution s an d have continued to be leaders in the field. W e have in mind especially John Harsanyi, Lloyd Shapley , Marti n Shubik , Rober t Aumann , an d Reinhar d Selte n (liste d i n order o f age) . I n additio n t o hi s contribution s t o gam e theor y an d economics , Robert Auman n als o made a numbe r o f significan t contribution s t o mathematics , including hi s thesis, "Asphericity o f Alternating Knots", Annais of Mathematics 6 4 (1956), pp. 374 - 392 and also : "Integrals o f Set-Value d Functions" , Journa l o f Mathematica l Analysi s an d Applications 1 2 (1965) , pp. 1-12 . "Measurable Utility and the Measurable Choic e Theorem", i n La Decision, Edi- tions d u Centr e Nationa l d e l a Recherche Scientifique , 1969 , pp. 15-26 , containin g Aumann's measurabl e selectio n theorem , "A Variational Problem Arisin g in Economics", Journal o f Mathematical Anal - ysis and Application s 1 1 (1965), pp.488-503 (wit h Mich a Perles), an d "Orderable Se t Function s an d Continuit y III : Orderability an d Absolut e Con - tinuity", SIA M Journal o n Contro l an d Optimizatio n 1 5 (1977), pp. 156-16 2 (wit h Uri Rothblum) . Finally, no listing, however partial, o f Aumann's contribution s to mathematic s can omi t "Values o f Non-Atomi c Games" , Princeto n Universit y Press , 1974 , x i - f 33 3 pp. (wit h Lloy d S . Shapley), which ha s le d to larg e numbers o f articles (on e appearing i n this volume) . Auman's publication s i n game theory bega n wit h "Acceptable Points in General Cooperativ e n-Person Games" , i n Contribution s to the Theory o f Games IV, Annais o f Math. Stud y 40, Princeton University Press , 1959, pp. 287-324 . In this insightfu l an d thought-provokin g wor k Aumann introduce d th e impor - tant concep t o f "acceptabl e points " fo r a game . I n a lette r t o th e edito r o f thi s volume, responding to a request t o reprint thi s paper, Bo b Aumann wrote : "There's a sof t spo t i n my heart fo r it: I t i s my first publishe d pape r in game theory proper. A t the time i t wa s published, I didn't realiz e that th e se t o f "acceptabl e points " i s simpl y th e beta-core . Thi s realization - o r better , reformulatio n - i s intimatel y relate d t o th e development o f the NTU theory , whic h cam e a year o r tw o later. " There ar e sof t spot s i n th e heart s o f man y gam e theorist s fo r Bo b Aumann , so w e are especiall y please d t o reprin t "Acceptabl e Point s i n Genera l Cooperativ e n-Person Games " i n this volume . vii viii PREFAC E

For a complet e lis t o f Aumann' s publication s throug h 1995 , se e Gam e an d Economic Theory : Selecte d Contribution s i n Hono r o f Robert J . Aumann , Sergi u Hart an d Abraha m Neyman , Editors , Universit y o f Michigan Press , June 1995 . A numbe r o f th e paper s i n th e curren t volume , o r relate d works , wer e pre - sented a t th e Field s Institut e Conferenc e "Ne w Direction s i n th e Theor y o f Mar - kets an d Games" , organize d b y Kennet h Arrow , Sergi u Hart , Andre u Mas-Colell , Jean-Francois Mertens, Walter Trockel , and Myrna Wooders (Chair) , held in honor of Robert Auman n i n 1995 . Th e program o f the Conferenc e conclude s the volume . In view o f Aumann's contributions to mathematics an d als o the social sciences, it i s most appropriat e tha t thi s Field s Institut e Communicatio n volum e b e i n hi s honor. I t i s with grea t pleasur e that th e contributor s an d th e edito r dedicat e thi s volume to Bo b Aumann .

Myrna H . Wooder s Editor

October 199 8 This page intentionally left blank Appendix

Presentations

at

The Field s Institute Worksho p

New Direction s i n the Theor y o f Market s an d Game s

October 1 9 - 23 , 199 5 Toronto, Ontario , Canad a

Joseph Abo u Tigh t Fre e Interaction: A Class o f Nash-Solvabl e Game Form s

Beth Alle n O n the Existenc e o f Cor e Allocations i n a Large Econom y with Incentiv e Compatibilit y Constraint s

C. D. Aliprantis, O . Burkinshaw an d K . C . Borde r Market Economie s

Robert M . Anderson an d Willia m R . Zam e Edgeworth's Conjectur e wit h Infinitel y Man y Commoditie s

Niels Anthonisen O n the Convergenc e o f Simpl e Learning to Equilibriu m in Game s

Daniel Arc e Aumann' s Microeconomics ? A Theory o f Fiscal Pact s

Robert J . Auman n Gam e Theor y i n The Rea l World: Hospita l Interns , Talmudic Bankruptc y Law , Spiderwebs , Oi l Lease Auctions , Formation o f Governments an d Othe r Storie s

Lawrence Ausube l an d Abiji t Se n Sequential Recontractin g Unde r Incomplet e Informatio n

Erik Balde r A Unifying Approac h t o Existence o f Nash Equilibri a

Vicky Barham an d Laur a Razzolin i From Eac h Accordin g to their Capacit y to Pay : Differentiate d Pricing i n Club s

285 286 Progra m

Dirk Bergeman n Learnin g an d Commitmen t i n Incentive Contract s

James Bergi n an d Joh n Dugga n Non-Cooperative Foundation s o f the Core : An Implementation-Theoretic Approac h

Volker Böh m Equilibri a fo r Exchang e Economie s an d fo r Game s o f

Exchange

Steven J . Bram s Modellin g Fre e Choic e i n Game s

Sandro Brusc o Perfec t Bayesia n Implementatio n i n Economic Environment s

Don Campbel l an d Jerr y Kell y A Trade-Of f Resul t fo r th e Gibbard-Sattherthwait e Theore m Subir Chakrabart i Pur e Strateg y Marko v Equilibri a i n Stochastic Game s wit h Many Player s

John Conle y Fundamenta l Nonconvexitie s i n Arrovian Market s an d a Coasian Solutio n to the Proble m o f Externalitie s

David Coope r Signalling , Adaptiv e Learnin g an d Equilibriu m Refinement s in an Entry Limi t Pricin g Gam e

Luis Corcho n an d Carme n Herrer o A Decent Proposa l

Ross Cressma n Shoul d Cheater s be Punished? Th e Surprisin g Find s in the Buyer-Selle r Gam e

Martin Cripp s an d Jonatha n Thoma s The Fol k Theore m i n Repeated Game s o f Incomplet e Information

Gabrielle Demang e Interi m Desig n o f Cor e Mechanism s

J. J . M . Derks an d H . H. Halle r Weighted Nucleol i

Egbert Dierke r an d Birgi t Groda l The Pric e Normalizatio n Proble m i n Imperfect Competitio n and the Objectiv e o f a Fir m

Victor Domansk y an d Victori a Krep s Explicit Solution s fo r a Clas s o f Repeated Game s wit h Incomplete Informatio n

Irinel Draga n O n Som e Relationships Betwee n the Shaple y Valu e and th e Banzhaf Valu e Appendix 287

Theo Driesse n Th e Assignmen t Problem : A Description o f Threats i n Terms o f Bargaining Range s Within an d Outsid e th e Cor e of the Assignmen t Gam e

John Dugga n Sequentiall y Rationa l Implementatio n wit h Incomplet e Information

Sjur Fla m Learnin g Economi c Equilibriu m

Wulf Gaertne r an d Nic k Baigen t Rationality an d Norms : Neve r Choos e the Uniquel y Larges t

Rod Garrat t an d Cheng-Zhon g Qi n On a Market fo r Coalition s wit h Indivisibl e Agent s an d Lotteries

Andrzej Grana s Som e Genera l Geometri e Principle s i n the Theor y o f KKM-Maps

Gordon Gree n Marke t Institution s an d Cor e Allocation s

Thomas A . Gresi k an d Eri c W. Bon d Information Sharin g Amon g Asymmetricall y Informe d Government s

Birgt Groda l an d Egber t Dierke r Maximization o f Shareholder's Rea l Wealt h

Peter Hammon d Multilaterall y Strategy-Proo f Mechanism s i n Rando m Aumann-Hildebrand Macroeconomie s

Sergiu Hart A Preliminary Communicatio n o n Pre-Play Communicatio n

Ebbe Hendon , Birgitt e Slot h an d Han s J0rge n Jacobse n Adaptive Learnin g i n Extensive For m Game s an d Sequentia l Equilibrium

Carmen Herrer o Persona l Right s and Collectiv e Ownership : The Rights-Egalitaria n Solutio n

Lu Hon g Proble m Solvin g b y Team s o f Heterogeneous Agent s

Charles Horvat h O n the Topologica l Choic e Proble m

Tatsuro Ichiish i A Profit-Centre Gam e with Incomplet e Informatio n

Matthew Jackso n an d Ehu d Kala i Recurring Game s an d Socia l Learnin g 288 Program

Mark Johnso n Algebrai c Automata , Strateg y Implementatio n an d Economic Consistenc y

Michael Jone s Cone s o f Cooperation fo r Indefinitel y Repeated , Generalize d Prisoner's Dilemm a Game s

Hans Keidin g an d Pete r Fristru p Strongly Implementabl e Socia l Choic e Correspondence s and th e Supernucleu s

Marc Kilgou r an d Steve n Bram s The True l

Hideo Konishi , Shlom o Weber an d Miche l L e Breto n Equilibrium i n a Model with Partia l Rivalr y

Van Kopii n Equitabl e Nonlinea r Pric e Regulatio n an d a n Alternativ e Approach t o Seria l Cos t Sharin g

Alexander Kovalenko v an d Myrn a Holt z Wooder s On Nonemptines s o f Approximate Core s o f Game s Without Sid e Payment s

Chantale LaCass e an d Ignatiu s Horstma n Dynamic Auction s with Learnin g

Ehud Lehre r Breakin g the Barrier s o f the Feasibl e Se t o n Repeate d Games with Differen t Tim e Preference s

Roger Lagunof f an d Akihik o Matsu i An "Anti-Folk " Theore m fo r a Clas s o f Asynchroneousl y Repeated Game s

Bart Lipma n Decisio n Theor y Without Logica l Omniscence s Towar d and Axiomati c Framewor k fo r Bounde d Rationalit y

Juan Enriqu e Martinez-Lega z

A New Characterizatio n o f Totally Balance d Game s

Kin Chun g L o Equilibriu m i n Belief s Unde r Uncertaint y

Richard McLea n Custome r Specifi c Aumann-Shaple y Price s

Jean-Franeois Merten s Relative Utilitarianis m Antoni Mesegue r an d Myrn a Holt z Wooder s NTU Games , Market s an d a Socia l Choic e Rul e Appendix 28 9

Paulo Monteiro , Frank Pag e an d Myrn a Holt z Wooder s Arbitrage an d Equilibriu m

Herve Moulin Thre e Additiv e Method s to Shar e Join t Cost s

Roger Myerso n Dua l Extraction i n Strategie-For m Game s

Matjaz Omladi c an d Vesn a Omladi c A Linear Alegebr a Approac h to Non-Transitiv e Expecte d Utility

Joseph Ostroy , L . Makowski an d Uz i Sega l Perfect Competitio n a s the Blueprin t fo r Efficienc y an d Incentive Compatibilit y

Frank Pag e an d Myrn a Holt z Wooder s Asymmetrie Information , th e Efficient y Cor e an d Stabl e Standards o f Behaviou r

Motty Perr y Implementatio n Withou t Commo n Prio r

Clara Ponsat i an d Jozse f Sakovics Mediation i s Necessary fo r Dynami c Efficienc y i n Bargainin g

Cheng-Zhong Qi n Th e Cor e o f an Economy : Edgewort h vs . Walra s

T. E . S . Raghavan Algorithm s fo r Locatin g the Nucleolu s fo r Specia l Classe s of Cooperative Game s

James Ratlif f Repeate d Game s with Privat e Informatio n abou t Duratio n

Lakshmi Rau t Aumann-Shaple y Rando m Orde r Valu e and Haa r Measur e

Laura Razzolin i an d Raja t De b Auction-Like Mechanism s fo r Pricin g Excludabl e Public Good s

Philip Ren y Loca l Payof T Security an d th e Existenc e o f Nash Equilibriu m in Discontinuous Game s

Arthur Robso n Adaptiv e Behaviour , Idiosyncrati c Ris k an d Aggregate Uncertaint y

Bryan Routledg e Artificia l Selection : Geneti c Algorithms an d Learnin g in a Rational Expectation s Mode l

Jozsef Sakovics Mirag e Equilibri a

Larry Samuelso n an d Ke n Binmor e Evolutionary Drif t an d Equilibriu m Selectio n 290 Program

David Schmeidler , Elchana n Ben-Porat h an d Itzha k Gilbo a Social Weifar e Unde r Uncertaint y

Norman Schofiel d Th e C- 1 Topolog y o n the Spac e o f Preference Profile s an d the Existenc e o f a Continuou s Preferenc e Aggregato r

Uzi Sega l Preference s Ove r Solution s to the Bargainin g Proble m

E. Somanathan Evolutionar y Stabilit y o f Pure-Strategy Equilibri a i n Finite Game s

Tayfun Sonme z Strategy-Proofnes s an d Singleto n Core s i n Generalize d Matching Problem s

Sylvain Sori n Strategi e Marke t Game s with Exchang e Rate s

Yeneng Su n an d Al i Kha n Integrals o f Set-Valued Function s with a Countable Range : Theory an d Application s

Jeroen Swinkel s an d Wolfgan g Pesendorfe r The Loser' s Curs e an d Informatio n Aggrega t ion i n Auction s

Rafael Tenori o an d Lind a Goldber g Strategie Behaviou r i n Two-Side d Foreig n Exchang e Auctions

William Thomso n Axiomati c Analysi s o f Allocation Problem s wit h Single-Peaked Preference s an d Individua l Endowment s

Arja Turunen-Re d Harsany i Aggregation , Arbitrag e an d the Cor e

Anne van de n Nouwelan d Consistency o f Equilibria i n Pure Exchang e Economie s an d Public Goo d Economie s

Antonio Villa r Classica l Equilibriu m wit h Increasin g Return s

Karl Vin d Perfec t Competitio n - Two Example s

Oscar Voli j an d Robert o Serran o Axiomatizations o f Neoclassical Concept s fo r Economie s

Jun Wak o Coalition-Proofnes s o f the Competitiv e Allocation s i n a Market wit h Indivisibl e Good s

Mark Walker , Jaso n Shacha t an d Ji m Co x An Experimental Tes t o f Bayesian vs . Adaptiv e Learnin g Appendix 29 1

John Weymar k Strategy-Proofednes s an d th e Tops-Onl y Propert y

Myrna Wooders , Fran k Pag e an d Paul o Monteir o Arbitrage an d Existenc e o f Equilibrium wit h Unbounde d Short Sale s

Shinji Yamashig e Bayesia n Approac h wit h Finit e Heirarchie s o f Beliefs : Bounded Rationalit y i n Strategie For m Game s

William Zam e Collatera l an d Default : A General Equilibriu m Vie w

Jiangang Zha o Th e Endogenizatio n o f Coalitio n Structure s i n Normal For m TU Game s