Epistemic game theory: reasoning and choice

582 Pages·2012·3.379 MB·English

by  Perea, Andrés

Epistemic Game Theory
Ineverydaylifewemustoftenreachdecisionswhileknowingthat
theoutcomewillnotonlydependonourownchoice,butalsoonthe
choicesofothers.Thesesituationsarethefocusofepistemicgame
theory.Unlikeclassicalgametheory,itexploreshowpeoplemay
reason about their opponents before they make their final choice
inagame.Packedwithexamplesandpracticalproblemsbasedon
storiesfromeverydaylife,thisisthefirsttextbooktoexplainthe
principlesofepistemicgametheory.Eachchapterisdedicatedto
oneparticular,naturalwayofreasoning.Thebookthenshowshow
eachofthesewaysofreasoningwillaffectthefinalchoicesthatcan
rationallybemade,andhowthesechoicescanbefoundbyiterative
procedures. Moreover, it does so in a way that uses elementary
mathematicsanddoesnotpresupposeanypreviousknowledgeof
gametheory.
andrés perea is Associate Professor in the Department of
QuantitativeEconomics,MaastrichtUniversity,TheNetherlands.
He has taught courses on epistemic game theory at several Euro-
peanuniversitiesandistheauthorofRationalityinExtensiveForm
Games(2001).

Epistemic Game Theory
Reasoning and Choice
Andrés Perea
cambridge university press
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©AndrésPerea2012
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Firstpublished2012
PrintedintheUnitedKingdomattheUniversityPress,Cambridge
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LibraryofCongressCataloguinginPublicationdata
Perea,Andrés.
Epistemicgametheory:reasoningandchoice/AndrésPerea.
pagescm
Includesbibliographicalreferencesandindex.
ISBN978-1-107-00891-5(hardback)–ISBN978-1-107-40139-6(paperback)
1. Gametheory. 2. Epistemiclogic. I. Title.
QA269.P4462012
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ISBN978-1-107-00891-5Hardback
ISBN978-1-107-40139-6Paperback
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Contents
Listoffigures page xi
Listoftables xiii
Acknowledgments xvii
1 Introduction 1
PartI Standardbeliefsinstaticgames
2 Beliefintheopponents’rationality 13
2.1 Beliefsabouttheopponent’schoice 13
2.2 Utilityfunctions 17
2.3 Morethantwoplayers 21
2.4 Choosingrationally 25
2.5 Strictlydominatedchoices 30
2.6 Beliefintheopponents’rationality 37
2.7 Graphicalmethod 45
2.8 Algorithm 46
2.9 Proofs 50
Practicalproblems 56
Theoreticalproblems 62
Literature 63
3 Commonbeliefinrationality 68
3.1 Beliefsabouttheopponents’beliefs 68
3.2 Beliefhierarchies 80
3.3 Epistemicmodel 85
3.4 Commonbeliefinrationality 91
3.5 Graphicalmethod 95
3.6 Existence 98
3.7 Algorithm 102
vii
viii Contents
3.8 Orderindependence 110
3.9 Proofs 112
Practicalproblems 118
Theoreticalproblems 123
Literature 124
4 Simplebeliefhierarchies 134
4.1 Simplebeliefhierarchies 134
4.2 Nashequilibrium 146
4.3 Computationalmethod 150
4.4 Beliefthatopponentsholdcorrectbeliefs 161
4.5 Proofs 167
Practicalproblems 171
Theoreticalproblems 175
Literature 177
PartII Lexicographicbeliefsinstaticgames
5 Primarybeliefintheopponent’srationality 187
5.1 Cautiousreasoningabouttheopponent 187
5.2 Lexicographicbeliefs 190
5.3 Beliefhierarchiesandtypes 195
5.4 Cautioustypes 199
5.5 Primarybeliefintheopponent’srationality 200
5.6 Commonfullbeliefin“primarybeliefinrationality” 202
5.7 Existence 210
5.8 Weaklydominatedchoices 213
5.9 Algorithm 215
5.10 Proofs 220
Practicalproblems 234
Theoreticalproblems 239
Literature 241
6 Respectingtheopponent’spreferences 250
6.1 Respectingtheopponent’spreferences 250
6.2 Commonfullbeliefin“respectofpreferences” 253
6.3 Existence 258
6.4 Whyeliminationofchoicesdoesnotwork 261
6.5 Preferencerestrictionsandlikelihoodorderings 263
6.6 Algorithm 269
6.7 Orderindependence 276
6.8 Proofs 278
Practicalproblems 292
Contents ix
Theoreticalproblems 296
Literature 298
7 Assumingtheopponent’srationality 301
7.1 Assumingtheopponent’srationality 301
7.2 Commonassumptionofrationality 305
7.3 Algorithm 314
7.4 Orderdependence 320
7.5 Proofs 321
Practicalproblems 332
Theoreticalproblems 337
Literature 339
PartIII Conditionalbeliefsindynamicgames
8 Beliefintheopponents’futurerationality 347
8.1 Beliefrevision 347
8.2 Dynamicgames 350
8.3 Conditionalbeliefs 358
8.4 Epistemicmodel 366
8.5 Beliefintheopponents’futurerationality 369
8.6 Commonbeliefinfuturerationality 375
8.7 Existence 379
8.8 Algorithm 383
8.9 Orderindependence 392
8.10 Backwardsorderofelimination 397
8.11 Backwardinduction 410
8.12 Gameswithunobservedpastchoices 419
8.13 Bayesianupdating 424
8.14 Proofs 428
Practicalproblems 447
Theoreticalproblems 453
Literature 454
9 Strongbeliefintheopponents’rationality 468
9.1 Strongbeliefintheopponents’rationality 468
9.2 Commonstrongbeliefinrationality 473
9.3 Algorithm 483
9.4 Comparisonwithbackwarddominanceprocedure 493
9.5 Orderdependence 501
9.6 Rationalityorderings 503
9.7 Bayesianupdating 514
9.8 Proofs 515