Behavioral Game Theory. Experiments in Strategic Interaction

558 Pages·2003·2.101 MB·english

by  Colin F. Camerer

Behavioral Game Theory
Experiments in Strategic Interaction
Colin F. Camerer
RussellSageFoundation,NewYork,NewYork
PrincetonUniversityPress,Princeton,NewJersey
Copyright©2003byRussellSageFoundation
PublishedbyPrincetonUniversityPress,
41WilliamStreet,
Princeton,NewJersey08540
IntheUnitedKingdom:PrincetonUniversityPress,
3MarketPlace,Woodstock,OxfordshireOX201SY
andRussellSageFoundation,
112East64thStreet,NewYork,NewYork10021
LibraryofCongressCataloging-in-PublicationData
Camerer,Colin,1959–
Behavioralgametheory:experimentsinstrategicinteraction/ColinF.Camerer.
p. cm.
Includesbibliographicreferencesandindex.
ISBN0-691-09039-4(alk.paper)
1. Gametheory. 2. Statisticaldecisions. 3. Negotiation—Mathematical
models. 4. Decisionmaking. I. Title. II. Series.
HB144.C364 2003
(cid:1) (cid:1)
330.015193—dc21 2002034642
BritishLibraryCataloging-in-PublicationDataisavailable
ThisbookwascomposedinITCNewBaskervillewithZzTEXbyPrincetonEditorial
Associates,Inc.,Scottsdale,Arizona
www.pup.princeton.edu
www.russellsage.org
PrintedintheUnitedStatesofAmerica
Contents
Preface xiii
1 Introduction 1
1.1 WhatIsGameTheoryGoodFor? 5
1.2 ThreeExamples 7
1.2.1 Example1:UltimatumBargaining 8
1.2.2 Example 2: Path-Dependent Coordination in
“ContinentalDivide”Games 12
1.2.3 Example3:“BeautyContests”andIterated
Dominance 16
1.3 ExperimentalRegularityandBehavioralGameTheory 20
1.4 Conclusion 24
Appendix 25
A1.1 BasicGameTheory 25
A1.2 ExperimentalDesign 34
2 Dictator,Ultimatum,andTrustGames 43
2.1 UltimatumandDictatorGames:BasicResults 48
2.2 MethodologicalVariables 59
2.2.1 Repetition 59
2.2.2 Methodology:Stakes 60
2.2.3 AnonymityandExperimenter“Blindness” 62
2.3 DemographicVariables 63
2.3.1 Gender 64
2.3.2 Race 65
2.3.3 AcademicMajor 65
2.3.4 Age 65
2.3.5 Brains,Biology,andBeauty 67
2.4 Culture 68
2.5 DescriptiveVariables:LabelingandContext 74
2.6 StructuralVariables 75
2.6.1 Identity,Communication,andEntitlement 76
2.6.2 CompetitivePressureandOutsideOptions 77
2.6.3 InformationabouttheAmountBeingDivided 78
2.6.4 MultipersonGames 80
2.6.5 Intentions:InfluenceofUnchosenAlternatives 81
2.7 TrustGames 83
2.7.1 IsTrustworthinessJustAltruism? 89
2.7.2 IndirectReciprocity,Karma,Culture 90
2.7.3 AComplexOmnibusGame 93
2.7.4 MultistageTrustGames 94
2.7.5 GiftExchangeinExperimentalLaborMarkets 95
2.8 Theory 101
2.8.1 PureandImpureAltruism 102
2.8.2 Inequality-AversionTheories 102
2.8.3 FairnessEquilibrium(Rabin) 105
2.8.4 Extensive-FormFairnessEquilibrium 107
2.8.5 ComparingApproaches 110
2.9 Conclusion 113
3 Mixed-StrategyEquilibrium 118
3.1 EarlyStudies 121
3.2 ModernStudies 125
3.3 SubjectiveRandomizationandMixedStrategies 134
3.4 ExplicitRandomization 138
3.5 PatentRaceandLocationGameswithMixedEquilibria 142
3.6 TwoFieldStudies 145
3.7 Conclusion 147
4 Bargaining 151
4.1 UnstructuredBargaining 153
4.1.1 UnstructuredBargainingoverTicketAllocations 153
4.1.2 Self-ServingInterpretationsofEvidencein
UnstructuredBargaining 158
4.2 StructuredBargaining 161
4.2.1 FiniteAlternating-OfferGames 161
4.2.2 LimitedComputation 167
4.2.3 RandomTermination 174
4.2.4 GameswithFixedDelayCostsandOutsideOptions 175
4.3 BargainingunderIncompleteInformation 182
4.3.1 One-SidedBuyerInformationwith
Seller-OnlyOffers 183
4.3.2 One-SidedPrivateInformationandStrikes 184
4.3.3 Sealed-BidMechanismsforBilateralBargaining 187
4.4 Conclusion 196
5 Dominance-SolvableGames 199
5.1 SimpleDominance-SolvableGames 203
5.1.1 GamesSolvablebyTwoStepsofIterated
Dominance 203
5.1.2 IteratedDominanceandTree-MatrixDifferences 205
5.1.3 APartiallyDominance-SolvablePatentRaceGame 208
5.2 BeautyContestGames 209
5.3 GamesinWhichIteratedReasoningDecreasesPayoffs 218
5.3.1 CentipedeGames 218
5.3.2 Prisoners’DilemmaandQuasi-CentipedeGames 221
5.3.3 PriceCompetition 223
5.3.4 TheTravelers’Dilemma 224
5.3.5 The“EmailGame” 226
5.3.6 AnImplementationMechanismThatUses
IteratedDominance 232
5.4 WhenMoreIterationIsBetter:The“DirtyFaces”Game 236
5.5 The“GrouchoMarx”TheoreminZero-Sum
Betting 239
5.6 StructuralModelsofDecisionRulesandLevelsof
Reasoning 242
5.7 Theories 254
5.7.1 MultipleTypes 254
5.7.2 Payoff-SensitiveNoisyIteration 255
5.7.3 QRERefinements:DifferencesandAsymmetry
inλ 255
5.7.4 APoissonCognitiveHierarchy 257
5.8 Conclusion 258
Appendix:RawChoicesinEmailGameand
AdditionalData 259
6 Learning 265
6.1 TheoriesofLearning 266
6.2 ReinforcementLearning 273
6.2.1 ReinforcementinWeak-LinkGames 274
6.2.2 ReinforcementwithPayoffVariability 275
6.2.3 Reinforcementwith“MoodShocks” 279
6.2.4 InformationConditions 279
6.3 BeliefLearning 283
6.3.1 WeightedFictitiousPlay 283
6.3.2 GeneralBeliefLearning 285
6.3.3 LearningDirectionTheory 288
6.3.4 BayesianLearning 290
6.3.5 MeasuringBeliefsDirectly 292
6.3.6 Population-LevelReplicatorDynamics 293
6.4 ImitationLearning 295
6.5 ComparativeStudies 298
6.5.1 ComparingBeliefModels 299
6.5.2 ComparingBeliefandReinforcementModels 299
6.6 Experience-WeightedAttraction(EWA)Learning 304
6.6.1 Example:ContinentalDivide 308
6.6.2 Example:p-BeautyContest,andSophistication 318
6.6.3 FunctionalEWA(fEWA) 322
6.7 RuleLearning 324
6.8 EconometricStudiesofEstimationProperties 330
6.9 Conclusions 332
7 Coordination 336
7.1 MatchingGames 341
7.1.1 AssignmentGamesandVisualSelection 345
7.1.2 UnpackingFocality 349
7.2 AsymmetricPlayers:BattleoftheSexes 353
7.2.1 OutsideOptions 355
7.2.2 Communication 356
7.2.3 EvolutionofMeaning 357
7.2.4 ExternalAssignment 362
7.2.5 Timing 365
7.3 MarketEntryGames 367
7.3.1 MultipleMarkets 371
7.3.2 Skill 372
7.4 Payoff-AsymmetricOrder-StatisticGames 375
7.4.1 ExperimentalEvidence 378
7.4.2 Weak-LinkGames 381
7.4.3 Mergers,BonusAnnouncements,and
“Leadership” 386
7.4.4 Median-ActionGames 388
7.4.5 PreplayAuctionsandEntryFees 390
7.4.6 GeneralOrder-StatisticGames 393
7.5 SelectingSelectionPrinciples 396
7.5.1 Simplicity 396
7.5.2 EmpiricalComparisonofSelectionPrinciples 398
7.6 Applications:Path-Dependence,MarketAdoption,and
CorporateCulture 399
7.6.1 Path-Dependence:CreatingaLaboratory
“ContinentalDivide” 399
7.6.2 MarketAdoption 400
7.6.3 Culture 402
7.7 Conclusion 403
Appendix:Psycholinguistics 405
8 SignalingandReputation 408
8.1 SimpleSignalingGamesandAdaptiveDynamics 411
8.2 SpecializedSignalingGames 427
8.2.1 Lobbying 427
8.2.2 CorporateFinance 430
8.2.3 GameswithRatchetEffects 436
8.2.4 BeliefLearninginLimitPricingSignalingGames 439
8.3 ReputationFormation 445
8.3.1 Trust 446
8.3.2 EntryDeterrence 453
8.3.3 LearninginRepeatedGames 458
8.4 Conclusion 462
9 Conclusion:WhatDoWeKnow,andWhereDoWeGo? 465
9.1 SummaryofResults 466
9.1.1 SimpleBargainingGames 466
9.1.2 Mixed-StrategyEquilibria 468
9.1.3 Bargaining 469
9.1.4 IteratedDominance 469
9.1.5 Learning 469
9.1.6 Coordination 470
9.1.7 Signaling 471
9.2 TopTenOpenResearchQuestions 473
Appendix:DesignDetails 477
References 497
Index 535
Preface
INECONOMICSATTHEUNIVERSITYOFCHICAGOinthelate1970s, gamethe-
orywasconsideredamessyanalyticalswampbetweenmonopolyandperfect
competition.Myintermediatepricetheoryteacherexplainedcynicallyhow
vonNeumannandMorgensternhadbothsolvedoneproblemthatwasno
longer a problem (by giving a method to measure utilities, which was not
neededaftertheordinalrevolution)andfailedtosolvethehardproblem
(uniquenessofequilibriuminallgames).Inclasswethereforestucktothe
importantpolarcasesandhopedthattwofirmswouldbeperfectlycompet-
itive,sowedidn’tneedgametheory.Fortunately,myfirstjobin1981(ade
factopostdoc)wasuptheroadatNorthwesternwhichhadanunbelievable
all-starteamofgametheoristsinitsMEDSDepartment—BengtHolmstrom,
Ehud Kalai, Paul Milgrom, Roger Myerson, John Roberts, Mark Satterth-
waite.Youcouldn’thelpbutlearnsomegametheory,andgetexcitedabout
it, just breathing the air in seminars. But my background in cognitive psy-
chology and behavioral decision research also made it natural to look at
gamesandaskhowpeoplewithcognitivelimitsandemotions—i.e.,normal
people—wouldbehave.
Sotherootsofthisbookgobackatleastthatfar.Aconferenceorganized
to honor Hilly Einhorn, who died tragically young, gave me a chance to
put ideas on paper (published in 1990) and coin the term “behavioral
game theory” for the empirical, descriptive approach rooted in data and
psychologicalfact.
Peoplewhohaveinfluencedmeintellectually(inlooselychronological
order) include my thesis advisors, Hilly and Robin Hogarth, Charlie Plott
(whotaughtaPh.D.courseatChicagoin1980whichchangedthecourseof
myresearch),KenMacCrimmon,HowardKunreuther,DanielKahneman,
PaulSlovic,AmosTversky,JohnKagel,GeorgeLoewenstein,JonBaron,Eric
Johnson,DickThaler,MatthewRabin,MarcKnez,TeckHo,KuanChong,
andmystudentsandmanyothercollaborators.
Thisbookhasbeenalongtimeinthemaking,andithasbenefitedfrom
ideas of many people. It was supported by a wonderful year at the Center
forAdvancedStudyintheBehavioralSciencesin1997–98.(Isitpossibleto
have a bad year there? It poured rain the whole time and it was still fun.)
Hundreds of seminar participants, and my colleagues in the MacArthur
NormsandPreferencesNetwork,haveshapedmythinkingovertheyears.
StudentsinmyPsychology101classatCaltech, colleaguesBrunoBroseta,
MiguelCosta-Gomes,JohnKennan,RobertoWeber,andinparticularVince
Crawford, and three anonymous referees all commented helpfully on the
manuscript. Research assistants Chris Anderson, Dan Clendenning, Ming
Hsu, and Angela Hung helped with graphics and editorial support. Gail
Nash, Rachel Kibble, and especially the tireless Karen Kerbs did amazing
workonthemanuscriptwithgreataplomb.ThanksalsotoPeterDougherty
of Princeton University Press for unflagging cheerleading, sage advice at
all the right moments, and some cool free books. Timely moral support
wasprovidedthroughoutbyPeter, andbyafortunecookiefromthelocal
Chinese delivery place. Their message arrived just before I finished the
tediousprocessofreviewingthecopyediting.Itsaid—nolie—“Youaresoon
toachieveperfection.”
The book is written so that the reader can either “dive” or “snorkel.”
Snorkelingmeansswimmingalongthesurface,lookingattheprettyfishbut
not going so deep that you need special equipment (e.g., intimate knowl-
edge of game theory) to breathe. Snorkelers should appreciate highlights
of crucial facts about what has been learned from experiments relative to
theory,andhowthosefindingssuggestnewtheory(summarizedinsection
summaries).Diverswillwanttoexplorethedetailsofstudiesandmaketheir
ownjudgmentsaboutwhatwaslearnedandimportant.
Ihavealsoskimpedon,oromitted,extremelyimportantareasbecause
theyareeitherwellcoveredelsewhereorsimplyoverwhelming—especially
experiments on cooperative games, unstructured bargaining (see Roth,
1995b, for more on this subject), public goods and prisoners’ dilemma
games,andauctions(seeKagel,1995,orKagelandLevin,inpress).
I have followed certain writing conventions. My goal is to convey the
regularities that have been discovered in experimental studies of game
theory, and a feeling for the care, craftsmanship, and conventions of the
experimentalmethod.Somestudieshavebeenoveremphasizedandsome
deemphasized. My preference is to describe the first or last studies and
the most solid or interesting results. In summarizing results, the goal is
full disclosure without clutter and irrelevance. If you are curious about a
detailoftheexperimentsordatathathavenotbeenreported,theyprobably
wereomittedbecausetheydonotmatter(orwereomittedintheoriginal
published reporting); however, I would be horrified if you took this as
an excuse to forgo looking at the original article if you are really curious.
For example, when the data from various periods of an experiment are
lumped together and reported as an average, that usually means there is
nointerestinglearningacrossperiods.
Details of how experiments are conducted (e.g., matching protocol,
incentivelevels)havebeencollectedintheappendixattheendofthebook
tokeepyoufrombeingdistractedasyouread.
Interestedinteachingfromthisbook?StartwithChapter1(duh)and
havethestudentsactuallyplaythethreegamesinthatchaptertogetafeel
for what piques their curiosity. Pick and choose other material to suit the
interestsandtechnicalmasteryofthestudents.Chapters2and7willbeof
broadest interest to noneconomists, Chapter 6 is heavy on econometrics,
andChapter8(andpartsofChapter4)isthemosttechnicallydemanding.