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Repeated Games and Reputations: Long-Run Relationships
by George J. Mailath (Author), Larry Samuelson (Author)
Hardcover: 672 pages
Publisher: Oxford University Press, USA (September 1, 2006)
Language: English
Review
"Repeated Games is comprehensive, self-contained, and extremely clear, with proofs that not infrequently improve on the originals. The book is an ideal text for part or all of a second graduate class in game theory, and will be a valuable aid for any student of the field."--Drew Fudenberg, Professor of Economics, Harvard University
"George Mailath and Larry Samuelson have written a landmark book in game theory, which takes stock of decades of research on repeated games and dynamic games more generally. The book not only provides an insightful synthesis of the extensive literatures relating to folk theorems, reputation, and play under a variety of information and monitoring structures; but perhaps more importantly it provides some original proofs that shed new light on some of the central results in these areas. This book will be an invaluable resource for researchers in the area, and should also quickly become a standard reading for advanced graduate students."--Matthew O. Jackson, Edie and Lew Wasserman Professor of Economics, California Institute of Technology
"The study of repeated games has been one of the most fruitful and important developments in economic theory in the last thirty years. In this beautifully lucid book, George Mailath and Larry Samuelson--two leading researchers in the field--lay out the classic results in detail and also bring the reader up to date with the latest findings."--Eric S. Maskin, A.O. Hirschman Professor of Social Science, Institute for Advanced Study
"The theory of reputations in repeated games has become one of the most important areas of research in economic theory, because it offers essential insights into the foundations of economic and political institutions. The past decade has seen great progress in this area, especially in the study of games with imperfect private monitoring. George Mailath and Larry Samuelson have been active leaders in this research, and here they systematically lay out the state of the art. This book will be an important text and reference for years to come."--Roger Myerson, University of Chicago
"Theorists use repeated games to understand self-enforcing contracts, and to explore the power of reputation formation in strategic settings. The centrality of these ideas explains why, despite the technical challenges involved, the literature on repeated games has grown rapidly in recent years. With their masterful treatment of many of the most important parts of this vast territory, Mailath and Samuelson have done a great service to both students and researchers."--David G. Pearce, Department of Economics, New York University
Book Description
Personalized and continuing relationships play a central role in any society. Economists have built upon the theories of repeated games and reputations to make important advances in understanding such relationships. Repeated Games and Reputations begins with a careful development of the fundamental concepts in these theories, including the notions of a repeated game, strategy, and equilibrium. Mailath and Samuelson then present the classic folk theorem and reputation results for games of perfect and imperfect public monitoring, with the benefit of the modern analytical tools of decomposability and self-generation. They also present more recent developments, including results beyond folk theorems and recent work in games of private monitoring and alternative approaches to reputations. Repeated Games and Reputations synthesizes and unifies the vast body of work in this area, bringing the reader to the research frontier. Detailed arguments and proofs are given throughout, interwoven with examples, discussions of how the theory is to be used in the study of relationships, and economic applications. The book will be useful to those doing basic research in the theory of repeated games and reputations as well as those using these tools in more applied research.
Contents
1 Introduction 1
1.1 Intertemporal Incentives 1
1.2 The Prisoners’ Dilemma 3
1.3 Oligopoly 4
1.4 The Prisoner’s Dilemma under Imperfect Monitoring 5
1.5 The Product-Choice Game 7
1.6 Discussion 8
1.7 A Reader’s Guide 10
1.8 The Scope of the Book 10
Part I Games with Perfect Monitoring
2 The Basic Structure of Repeated Games with Perfect Monitoring 15
2.1 The Canonical Repeated Game 15
2.1.1 The Stage Game 15
2.1.2 Public Correlation 17
2.1.3 The Repeated Game 19
2.1.4 Subgame-Perfect Equilibrium of the Repeated Game 22
2.2 The One-Shot Deviation Principle 24
2.3 Automaton Representations of Strategy Profiles 29
2.4 Credible Continuation Promises 32
2.5 Generating Equilibria 37
2.5.1 Constructing Equilibria: Self-Generation 37
2.5.2 Example: Mutual Effort 40
2.5.3 Example: The Folk Theorem 41
2.5.4 Example: Constructing Equilibria for Low δ 44
2.5.5 Example: Failure of Monotonicity 46
2.5.6 Example: Public Correlation 49
2.6 Constructing Equilibria: Simple Strategies and Penal Codes 51
2.6.1 Simple Strategies and Penal Codes 51
2.6.2 Example: Oligopoly 54
2.7 Long-Lived and Short-Lived Players 61
2.7.1 Minmax Payoffs 63
2.7.2 Constraints on Payoffs 66
x Contents
3 The Folk Theorem with Perfect Monitoring 69
3.1 Examples 70
3.2 Interpreting the Folk Theorem 72
3.2.1 Implications 72
3.2.2 Patient Players 73
3.2.3 Patience and Incentives 75
3.2.4 Observable Mixtures 76
3.3 The Pure-Action Folk Theorem for Two Players 76
3.4 The Folk Theorem with More than Two Players 80
3.4.1 A Counterexample 80
3.4.2 Player-Specific Punishments 82
3.5 Non-Equivalent Utilities 87
3.6 Long-Lived and Short-Lived Players 91
3.7 Convexifying the Equilibrium Payoff SetWithout
Public Correlation 96
3.8 Mixed-Action Individual Rationality 101
4 How Long Is Forever? 105
4.1 Is the Horizon Ever Infinite? 105
4.2 Uncertain Horizons 106
4.3 Declining Discount Factors 107
4.4 Finitely Repeated Games 112
4.5 Approximate Equilibria 118
4.6 Renegotiation 120
4.6.1 Finitely Repeated Games 122
4.6.2 Infinitely Repeated Games 134
5 Variations on the Game 145
5.1 Random Matching 145
5.1.1 Public Histories 146
5.1.2 Personal Histories 147
5.2 Relationships in Context 152
5.2.1 A Frictionless Market 153
5.2.2 Future Benefits 154
5.2.3 Adverse Selection 155
5.2.4 Starting Small 158
5.3 Multimarket Interactions 161
5.4 Repeated Extensive Forms 162
5.4.1 Repeated Extensive-Form Games Have More Subgames 163
5.4.2 Player-Specific Punishments in Repeated Extensive-Form
Games 165
5.4.3 Extensive-Form Games and Imperfect Monitoring 167
5.4.4 Extensive-Form Games and Weak Individual Rationality 168
5.4.5 Asynchronous Moves 169
5.4.6 Simple Strategies 172
Contents xi
5.5 Dynamic Games: Introduction 174
5.5.1 The Game 175
5.5.2 Markov Equilibrium 177
5.5.3 Examples 178
5.6 Dynamic Games: Foundations 186
5.6.1 Consistent Partitions 187
5.6.2 Coherent Consistency 188
5.6.3 Markov Equilibrium 190
5.7 Dynamic Games: Equilibrium 192
5.7.1 The Structure of Equilibria 192
5.7.2 A Folk Theorem 195
6 Applications 201
6.1 PriceWars 201
6.1.1 Independent Price Shocks 201
6.1.2 Correlated Price Shocks 203
6.2 Time Consistency 204
6.2.1 The Stage Game 204
6.2.2 Equilibrium, Commitment, and Time Consistency 206
6.2.3 The Infinitely Repeated Game 207
6.3 Risk Sharing 208
6.3.1 The Economy 209
6.3.2 Full Insurance Allocations 210
6.3.3 Partial Insurance 212
6.3.4 Consumption Dynamics 213
6.3.5 Intertemporal Consumption Sensitivity 219
Part II Games with (Imperfect) Public Monitoring
7 The Basic Structure of Repeated Games with Imperfect Public
Monitoring 225
7.1 The Canonical Repeated Game 225
7.1.1 The Stage Game 225
7.1.2 The Repeated Game 226
7.1.3 Recovering a Recursive Structure: Public Strategies and
Perfect Public Equilibria 228
7.2 A Repeated Prisoners’ Dilemma Example 232
7.2.1 Punishments Happen 233
7.2.2 Forgiving Strategies 235
7.2.3 Strongly Symmetric Behavior Implies Inefficiency 239
7.3 Decomposability and Self-Generation 241
7.4 The Impact of Increased Precision 249
7.5 The Bang-Bang Result 251