Repeated games with incomplete information:
During the height of the Cold War, between 1965 and 1968, Robert Aumann, Michael Maschler, and Richard Stearns collaborated on research on the dynamics of arms control negotiations that has since become foundational to work on repeated games. These five seminal papers are collected here for the firs...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge, Mass. u.a.
MIT Press
1995
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Summary: | During the height of the Cold War, between 1965 and 1968, Robert Aumann, Michael Maschler, and Richard Stearns collaborated on research on the dynamics of arms control negotiations that has since become foundational to work on repeated games. These five seminal papers are collected here for the first time, with the addition of "postscripts" describing many of the developments since the papers were written. The basic model studied throughout the book is one in which players ignorant about the game being played must learn what they can from the actions of the others. |
| Physical Description: | XVII, 342 S. graph. Darst. |
| ISBN: | 0262011476 |
Staff View
MARC
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| 520 | 3 | |a During the height of the Cold War, between 1965 and 1968, Robert Aumann, Michael Maschler, and Richard Stearns collaborated on research on the dynamics of arms control negotiations that has since become foundational to work on repeated games. These five seminal papers are collected here for the first time, with the addition of "postscripts" describing many of the developments since the papers were written. The basic model studied throughout the book is one in which players ignorant about the game being played must learn what they can from the actions of the others. | |
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Record in the Search Index
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|---|---|
| adam_text | Contents
Preface xi
Chapter One
Game Theoretic Aspects of Gradual
Disarmament
1 Introduction 1
2 A Case When a Player Cannot Benefit in
the Long Run from His Information 3
3 A Case When a Player Should Disclose His
Information 10
4 A Case When a Player Should Partially Disclose
His Information 11
5 The Main Theorem 22
6 The Optimal Strategy of Player 2 34
7 Conclusions 38
8 Where Do We Go Prom Here? 39
Postscripts
a Martingales 42
b Convexity and Concavity as Monotonicity
in Information 43
c The Error Term 44
d Optimal Strategies of the Uninformed
Player 53
e Monotonicity of vn and the Recursive
Structure of Tn 61
Chapter Two
Repeated Games with Incomplete Information:
A Survey of Recent Results
1 Introduction 65
2 Repeated Games and the Problem of
Information 66
viii Contents
3 Lack of Information on One Side—Stage Games
in Normal Form 70
3.1 The Model 70
3.2 Description of Ai(p) 75
3.3 Revealing Information 76
3.4 The Main Theorem 78
3.5 The Optimal Strategy of Player 1 81
3.6 The Optimal Strategy of Player 2 87
4 Lack of Information on Both Sides 91
4.1 The Model 91
4.2 The Independent and the Dependent
Cases 100
4.3 Conditions Under Which a Value
Exists 105
5 Incomplete Knowledge of Moves 110
5.1 Examples 110
5.2 The Model 122
5.3 Revealing Information 125
5.4 The Main Theorem 127
6 Further Problems 129
Postscripts
a Incomplete Information on Both Sides:
limi;n 130
b Incomplete Information on Both Sides:
The Limit of the Discounted Values 130
c The Conceptual Distinction Between
Too and Fn: Generalities 131
d The Conceptual Distinction Between
Too and Fn: Incomplete Information 136
e Non Zero Sum Games 137
f Discounting 139
g Continuous Time 140
h Alternative Definitions of Value, Maxmin,
and Minmax in T^ 140
i Incomplete Information on Both Sides:
The Dependent Case 143
j Incomplete Information on
One and a Half Sides 145
Contents ix
Chapter Three
A Formal Information Concept for Games
with Incomplete Information 155
Chapter Four
Repeated Games of Incomplete Information:
The Zero Sum Extensive Case
1 Introduction 175
2 Motivation 176
3 The Mathematical Model 177
4 Examples 181
5 The Infinite Stage Game and its Relation
to the ri Stage Games 186
6 Statement of the Main Theorem: The Value
of the Infinite Stage Game 188
7 Proof of the Main Theorem 191
Postscripts
a Monotonicity of vn and the Informed
Player s Information Matrices 206
b Remembering One s Own Moves 211
c Optimal Strategies for the Uninformed
Player 212
d The Case When P2 Knows His Payoff 212
e The Error Term 213
f Incomplete Information on Both Sides 215
g Both Players Have Incomplete Information
and Know Their Own Payoffs 216
h Identical Information 216
i Games Without a Recursive Structure 219
Chapter Five
Repeated Games of Incomplete Information:
An Approach to the Non Zero Sum Case
1 Introduction 223
2 Equilibrium Points and Equilibrium Payoffs
in a 2 Player One Shot Game 226
x Contents
3 Equilibrium Payoffs of an
Infinitely Repeated 2 Player Game
with Complete Information 233
4 Repeated Games with Incomplete
Information 240
5 The Possibility of Cheating 257
6 Joint Plans 260
7 More Equilibrium Points 269
8 More Equilibrium Payoffs 277
Postscripts
a Existence of Equilibria 294
b The Folk Theorem and Individual
Rationality 294
c Characterization of Equilibria:
Background 294
d Characterization of Equilibria:
Geometric Preliminaries 296
e Characterization of Equilibria:
Precise Formulation 298
f Characterization of Equilibria:
Outline of Hart s Proof 301
g An Economic Example Requiring
Unboundedly Many Communications 311
h Known Own Payoffs 320
i Communication Equilibria 320
j Perturbations 321
Bibliography 323
Index 335
|
| any_adam_object | 1 |
| author | Aumann, Robert J. 1930- Maschler, Michael B. |
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| author_sort | Aumann, Robert J. 1930- |
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| callnumber-first | J - Political Science |
| callnumber-label | JX1974 |
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| dewey-full | 327.1/74/015193 |
| dewey-hundreds | 300 - Social sciences |
| dewey-ones | 327 - International relations |
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| dewey-search | 327.1/74/015193 |
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| dewey-tens | 320 - Political science (Politics and government) |
| discipline | Informatik Politologie Mathematik Militärwissenschaft Wirtschaftswissenschaften |
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| illustrated | Illustrated |
| indexdate | 2024-07-09T17:50:43Z |
| institution | BVB |
| isbn | 0262011476 |
| language | English |
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| spelling | Aumann, Robert J. 1930- Verfasser (DE-588)119302306 aut Repeated games with incomplete information Robert J. Aumann and Michael B. Maschler Cambridge, Mass. u.a. MIT Press 1995 XVII, 342 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier During the height of the Cold War, between 1965 and 1968, Robert Aumann, Michael Maschler, and Richard Stearns collaborated on research on the dynamics of arms control negotiations that has since become foundational to work on repeated games. These five seminal papers are collected here for the first time, with the addition of "postscripts" describing many of the developments since the papers were written. The basic model studied throughout the book is one in which players ignorant about the game being played must learn what they can from the actions of the others. Armements - Contrôle - Simulation, Méthodes de Desarme - Simulación - Métodos Désarmement - Simulation, Méthodes de Jeux, Théorie des Juegos, Teoría de los Ontwapening gtt Speltheorie gtt Wapenbeheersing gtt Arms control Simulation methods Disarmament Simulation methods Game theory Rüstungsbegrenzung (DE-588)4115804-0 gnd rswk-swf Spieltheorie (DE-588)4056243-8 gnd rswk-swf Abrüstung (DE-588)4000197-0 gnd rswk-swf Unvollkommene Information (DE-588)4140474-9 gnd rswk-swf Simulation (DE-588)4055072-2 gnd rswk-swf Abrüstung (DE-588)4000197-0 s Unvollkommene Information (DE-588)4140474-9 s Simulation (DE-588)4055072-2 s DE-604 Rüstungsbegrenzung (DE-588)4115804-0 s Spieltheorie (DE-588)4056243-8 s DE-188 Maschler, Michael B. Verfasser aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006878870&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Aumann, Robert J. 1930- Maschler, Michael B. Repeated games with incomplete information Armements - Contrôle - Simulation, Méthodes de Desarme - Simulación - Métodos Désarmement - Simulation, Méthodes de Jeux, Théorie des Juegos, Teoría de los Ontwapening gtt Speltheorie gtt Wapenbeheersing gtt Arms control Simulation methods Disarmament Simulation methods Game theory Rüstungsbegrenzung (DE-588)4115804-0 gnd Spieltheorie (DE-588)4056243-8 gnd Abrüstung (DE-588)4000197-0 gnd Unvollkommene Information (DE-588)4140474-9 gnd Simulation (DE-588)4055072-2 gnd |
| subject_GND | (DE-588)4115804-0 (DE-588)4056243-8 (DE-588)4000197-0 (DE-588)4140474-9 (DE-588)4055072-2 |
| title | Repeated games with incomplete information |
| title_auth | Repeated games with incomplete information |
| title_exact_search | Repeated games with incomplete information |
| title_full | Repeated games with incomplete information Robert J. Aumann and Michael B. Maschler |
| title_fullStr | Repeated games with incomplete information Robert J. Aumann and Michael B. Maschler |
| title_full_unstemmed | Repeated games with incomplete information Robert J. Aumann and Michael B. Maschler |
| title_short | Repeated games with incomplete information |
| title_sort | repeated games with incomplete information |
| topic | Armements - Contrôle - Simulation, Méthodes de Desarme - Simulación - Métodos Désarmement - Simulation, Méthodes de Jeux, Théorie des Juegos, Teoría de los Ontwapening gtt Speltheorie gtt Wapenbeheersing gtt Arms control Simulation methods Disarmament Simulation methods Game theory Rüstungsbegrenzung (DE-588)4115804-0 gnd Spieltheorie (DE-588)4056243-8 gnd Abrüstung (DE-588)4000197-0 gnd Unvollkommene Information (DE-588)4140474-9 gnd Simulation (DE-588)4055072-2 gnd |
| topic_facet | Armements - Contrôle - Simulation, Méthodes de Desarme - Simulación - Métodos Désarmement - Simulation, Méthodes de Jeux, Théorie des Juegos, Teoría de los Ontwapening Speltheorie Wapenbeheersing Arms control Simulation methods Disarmament Simulation methods Game theory Rüstungsbegrenzung Spieltheorie Abrüstung Unvollkommene Information Simulation |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006878870&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT aumannrobertj repeatedgameswithincompleteinformation AT maschlermichaelb repeatedgameswithincompleteinformation |