Economics and the Theory of Games

526 Pages·2003·7.49 MB·English

by  Fernando Vega-Redondo

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Economicsandthetheoryofgames
This textbook offers a systematic, self-contained account of the main contribu-
tions of modern game theory and its applications to economics. Starting with a
detaileddescriptionofhowtomodelstrategicsituations,thediscussionproceeds
bystudyingbasicsolutionconcepts,theirmainrefinements,gamesplayedunder
incompleteinformation,andrepeatedgames.Foreachofthesetheoreticaldevel-
opments,thereisacompanionsetofapplicationsthatcoverthemostrepresentative
instancesofgame-theoreticanalysisineconomics,e.g.,oligopolisticcompetition,
public goods, coordination failures, bargaining, insurance markets, implementa-
tion theory, signaling, and auctions. The theory and applications covered in the
first part of the book fall under the so-called classical approach to game theory,
which is founded on the paradigm of players’ unlimited rationality. The second
partshiftstowardtopicsthatnolongerabidebythatparadigm.Thisleadstothe
studyofimportanttopicssuchastheinterplaybetweenevolutionandrationality,
thebehavioraldynamicsinducedbysociallearning,andhowplayersmighttackle
theproblemofmultipleequilibria.
FernandoVega-RedondoiscurrentlyProfessorattheUniversidaddeAlicanteand
theUniversitatPompeuFabra.Hisrecentresearchhasfocusedonbothgamethe-
oryandlearningandotherinterdisciplinaryfieldssuchasevolutionandComplex
networks.Hispapershavebeenpublishedinawidearrayofinfluentialjournals
including Econometrica, Journal of Economic Theory, International Economic
Review,GamesandEconomicBehavior,EconomicTheory,JournalofTheoretical
Biology, and Physical Review Letters. Professor Vega-Redondo is author of the
book Evolution, Games and Economic Behavior and the Spanish-language text-
book Econom´ıa y Juegos: Teor´ıa y Aplicaciones. He has been a visiting scholar
at the Indian Statistical Institute; the Institute for Advanced Studies in Vienna;
theHebrewUniversityofJerusalem;andtheUniversitiesofHarvard,California–
SanDiego,andBoston.Heisco-editorofSpanishEconomicReviewandmember
oftheEditorialBoardofLectureNotesinEconomicsandMathematicalSystems.
ProfessorVega-RedondoreceivedhisPh.D.fromtheUniversityofMinnesota.

Economics and the theory
of games
FERNANDO VEGA-REDONDO
UniversidaddeAlicanteandUniversitat
PompeuFabra,Spain
ToOlalla,
whohappilyenteredthegameasIwascompletingthelast
stagesofthisbook

  
Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore, São Paulo
Cambridge University Press
The Edinburgh Building, Cambridge  , United Kingdom
Published in the United States of America by Cambridge University Press, New York
www.cambridge.org
Information on this title: www.cambridge.org/9780521772518
© Fernando Vega-Redondo 2003
This book is in copyright. Subject to statutory exception and to the provision of
relevant collective licensing agreements, no reproduction of any part may take place
without the written permission of Cambridge University Press.
First published in print format 2003
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Contents
Preface pagexi
1 Theoreticalframework 1
1.1 Introductionandexamples 1
1.2 Representationofagameinextensiveform 4
1.3 Representationofagameinstrategicform 12
1.4 Mixedextensionofagame 16
Supplementarymaterial 18
1.5 Mixedandbehavioralstrategies 18
1.6 Representationofagameincoalitionalform 23
Summary 26
Exercises 26
2 Strategic-formanalysis:theory 30
2.1 Dominanceanditerativedominance 30
2.2 Nashequilibrium 35
2.3 Zero-sumbilateralgames 45
Supplementarymaterial 50
2.4 Nashequilibrium:formalexistenceresults 50
2.5 Strongandcoalition-proofequilibria 53
2.6 Correlatedequilibrium 56
2.7 Rationalizability 61
Summary 68
Exercises 69
3 Strategic-formanalysis:applications 72
3.1 Oligopoly(I):staticmodels 72
3.2 Mechanismdesign(I):efficientallocationofpublicgoods 83
3.3 Mechanismdesign(II):Nashimplementation 90
3.4 Markets(I):macroeconomiccoordinationfailures 99
Summary 104
Exercises 105
4 RefinementsofNashequilibrium:theory 110
4.1 Introduction 110
4.2 Refinementsexcluding“incrediblethreats”:examples 110
4.3 Subgame-perfectequilibrium 115
4.4 WeakperfectBayesianequilibrium 117
Supplementarymaterial 120
vii
viii Contents
4.5 Refinementsexcluding“untenablebeliefs”:examples 120
4.6 Sequentialequilibrium 128
4.7 Perfectandproperequilibria 131
4.8 Strategic-formrefinements 135
Summary 143
Exercises 144
5 RefinementsofNashequilibrium:applications 151
5.1 Oligopoly(II):sequentialmoves 151
5.2 Markets(II):decentralizedpriceformation 159
5.3 Oligopoly(III):differentiatedproducts 171
5.4 Mechanismdesign(III):efficientallocationofanindivisibleobject 176
Summary 182
Exercises 184
6 Incompleteinformation:theory 188
6.1 Introductionandexamples 188
6.2 Bayesiangames 191
6.3 Bayes-Nashequilibrium 196
6.4 Signalinggames 204
Supplementarymaterial 217
6.5 Mixedstrategies,revisited:apurificationapproach 217
6.6 Forwardinduction 221
Summary 225
Exercises 226
7 Incompleteinformation:applications 231
7.1 Markets(III):signalinginthelabormarket 231
7.2 Markets(IV):insurancemarketsandadverseselection 244
7.3 Mechanismdesign(IV):one-sidedauctions 254
7.4 Mechanismdesign(V):buyer–sellertrade 267
Summary 275
Exercises 276
8 Repeatedinteraction:theory 281
8.1 Introductionandexamples 281
8.2 Repeatedgames:basictheoreticalframework 283
8.3 Folktheorems:Nashequilibrium 286
8.4 Reputationand“irrationality”:informaldiscussion 294
Supplementarymaterial 300
8.5 Folktheorems:subgame-perfectequilibrium 300
8.6 Reputationand“irrationality”:formalanalysis 311
Summary 319
Exercises 321
9 Repeatedinteraction:applications 324
9.1 Oligopoly(IV):intertemporalcollusioninaCournotscenario 324
9.2 Oligopoly(V):intertemporalcollusioninaBertrandscenario 334
9.3 Markets(V):efficiencywagesandunemployment 341
Summary 351
Exercises 352