Repeated Games and Reputations Long-Run Relationships

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Format: Hardcover
Pub. Date: 2006-09-28
Publisher(s): Oxford University Press
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Summary

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 thefundamental 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 ofdecomposability 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 thisarea, 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 thetheory of repeated games and reputations as well as those using these tools in more applied research.

Author Biography


George J. Mailath (Ph. D., Princeton University) is the Walter H. Annenberg Professor in the Social Sciences at the University of Pennsylvania. Larry Samuelson (Ph. D., University of Illinois) is the Antoine Augustin Cournot Professor of Economics at the University of Wisconsin.

Table of Contents

Introduction
1(14)
Intertemporal Incentives
1(2)
The Prisoners' Dilemma
3(1)
Oligopoly
4(1)
The Prisoner's Dilemma under Imperfect Monitoring
5(2)
The Product-Choice Game
7(1)
Discussion
8(2)
A Reader's Guide
10(1)
The Scope of the Book
10(5)
Part I Games with Perfect Monitoring
The Basic Structure of Repeated Games with Perfect Monitoring
15(54)
The Canonical Repeated Game
15(9)
The Stage Game
15(2)
Public Correlation
17(2)
The Repeated Game
19(3)
Subgame-Perfect Equilibrium of the Repeated Game
22(2)
The One-Shot Deviation Principle
24(5)
Automaton Representations of Strategy Profiles
29(3)
Credible Continuation Promises
32(5)
Generating Equilibria
37(14)
Constructing Equilibria: Self-Generation
37(3)
Example: Mutual Effort
40(1)
Example: The Folk Theorem
41(3)
Example: Constructing Equilibria for Low δ
44(2)
Example: Failure of Monotonicity
46(3)
Example: Public Correlation
49(2)
Constructing Equilibria: Simple Strategies and Penal Codes
51(10)
Simple Strategies and Penal Codes
51(3)
Example: Oligopoly
54(7)
Long-Lived and Short-Lived Players
61(8)
Minmax Payoffs
63(3)
Constraints on Payoffs
66(3)
The Folk Theorem with Perfect Monitoring
69(36)
Examples
70(2)
Interpreting the Folk Theorem
72(4)
Implications
72(1)
Patient Players
73(2)
Patience and Incentives
75(1)
Observable Mixtures
76(1)
The Pure-Action Folk Theorem for Two Players
76(4)
The Folk Theorem with More than Two Players
80(7)
A Counterexample
80(2)
Player-Specific Punishments
82(5)
Non-Equivalent Utilities
87(4)
Long-Lived and Short-Lived Players
91(5)
Convexifying the Equilibrium Payoff Set Without Public Correlation
96(5)
Mixed-Action Individual Rationality
101(4)
How Long Is Forever?
105(40)
Is the Horizon Ever Infinite?
105(1)
Uncertain Horizons
106(1)
Declining Discount Factors
107(5)
Finitely Repeated Games
112(6)
Approximate Equilibria
118(2)
Renegotiation
120(25)
Finitely Repeated Games
122(12)
Infinitely Repeated Games
134(11)
Variations on the Game
145(56)
Random Matching
145(7)
Public Histories
146(1)
Personal Histories
147(5)
Relationships in Context
152(9)
A Frictionless Market
153(1)
Future Benefits
154(1)
Adverse Selection
155(3)
Starting Small
158(3)
Multimarket Interactions
161(1)
Repeated Extensive Forms
162(12)
Repeated Extensive-Form Games Have More Subgames
163(2)
Player-Specific Punishments in Repeated Extensive-Form Games
165(2)
Extensive-Form Games and Imperfect Monitoring
167(1)
Extensive-Form Games and Weak Individual Rationality
168(1)
Asynchronous Moves
169(3)
Simple Strategies
172(2)
Dynamic Games: Introduction
174(12)
The Game
175(2)
Markov Equilibrium
177(1)
Examples
178(8)
Dynamic Games: Foundations
186(6)
Consistent Partitions
187(1)
Coherent Consistency
188(2)
Markov Equilibrium
190(2)
Dynamic Games: Equilibrium
192(9)
The Structure of Equilibria
192(3)
A Folk Theorem
195(6)
Applications
201(24)
Price Wars
201(3)
Independent Price Shocks
201(2)
Correlated Price Shocks
203(1)
Time Consistency
204(4)
The Stage Game
204(2)
Equilibrium, Commitment, and Time Consistency
206(1)
The Infinitely Repeated Game
207(1)
Risk Sharing
208(17)
The Economy
209(1)
Full Insurance Allocations
210(2)
Partial Insurance
212(1)
Consumption Dynamics
213(6)
Intertemporal Consumption Sensitivity
219(6)
Part II Games with (Imperfect) Public Monitoring
The Basic Structure of Repeated Games with Imperfect Public Monitoring
225(48)
The Canonical Repeated Game
225(7)
The Stage Game
225(1)
The Repeated Game
226(2)
Recovering a Recursive Structure: Public Strategies and Perfect Public Equilibria
228(4)
A Repeated Prisoners' Dilemma Example
232(9)
Punishments Happen
233(2)
Forgiving Strategies
235(4)
Strongly Symmetric Behavior Implies Inefficiency
239(2)
Decomposability and Self-Generation
241(8)
The Impact of Increased Precision
249(2)
The Bang-Bang Result
251(4)
An Example with Short-Lived Players
255(9)
Perfect Monitoring
256(4)
Imperfect Public Monitoring of the Long-Lived Player
260(4)
The Repeated Prisoners' Dilemma Redux
264(5)
Symmetric Inefficiency Revisited
264(3)
Enforcing a Mixed-Action Profile
267(2)
Anonymous Players
269(4)
Bounding Perfect Public Equilibrium Payoffs
273(20)
Decomposing on Half-Spaces
273(5)
The Inefficiency of Strongly Symmetric Equilibria
278(2)
Short-Lived Players
280(2)
The Upper Bound on Payoffs
280(1)
Binding Moral Hazard
281(1)
The Prisoners' Dilemma
282(11)
Bounds on Efficiency: Pure Actions
282(2)
Bounds on Efficiency: Mixed Actions
284(3)
A Characterization with Two Signals
287(2)
Efficiency with Three Signals
289(2)
Efficient Asymmetry
291(2)
The Folk Theorem with Imperfect Public Monitoring
293(36)
Characterizing the Limit Set of PPE Payoffs
293(5)
The Rank Conditions and a Public Monitoring Folk Theorem
298(5)
Perfect Monitoring Characterizations
303(2)
The Folk Theorem with Long-Lived Players
303(1)
Long-Lived and Short-Lived Players
303(2)
Enforceability and Identifiability
305(4)
Games with a Product Structure
309(2)
Repeated Extensive-Form Games
311(5)
Games of Symmetric Incomplete Information
316(10)
Equilibrium
318(2)
A Folk Theorem
320(6)
Short Period Length
326(3)
Private Strategies in Games with Imperfect Public Monitoring
329(18)
Sequential Equilibrium
329(2)
A Reduced-Form Example
331(3)
Pure Strategies
331(1)
Public Correlation
332(1)
Mixed Public Strategies
332(1)
Private Strategies
333(1)
Two-Period Examples
334(6)
Equilibrium Punishments Need Not Be Equilibria
334(3)
Payoffs by Correlation
337(1)
Inconsistent Beliefs
338(2)
An Infinitely Repeated Prisoner's Dilemma
340(7)
Public Transitions
340(3)
An Infinitely Repeated Prisoners' Dilemma: Indifference
343(4)
Applications
347(38)
Oligopoly with Imperfect Monitoring
347(7)
The Game
347(1)
Optimal Collusion
348(2)
Which News Is Bad News?
350(2)
Imperfect Collusion
352(2)
Repeated Adverse Selection
354(11)
General Structure
354(1)
An Oligopoly with Private Costs: The Game
355(1)
A Uniform-Price Equilibrium
356(1)
A Stationary-Outcome Separating Equilibrium
357(2)
Efficiency
359(1)
Nonstationary-Outcome Equilibria
360(5)
Risk Sharing
365(5)
Principal-Agent Problems
370(15)
Hidden Actions
370(1)
Incomplete Contracts: The Stage Game
371(1)
Incomplete Contracts: The Repeated Game
372(2)
Risk Aversion: The Stage Game
374(1)
Risk Aversion: Review Strategies in the Repeated Game
375(10)
Part III Games with Private Monitoring
Private Monitoring
385(30)
A Two-Period Example
385(9)
Almost Public Monitoring
387(2)
Conditionally Independent Monitoring
389(3)
Intertemporal Incentives from Second-Period Randomization
392(2)
Private Monitoring Games: Basic Structure
394(3)
Almost Public Monitoring: Robustness in the Infinitely Repeated Prisoner's Dilemma
397(7)
The Forgiving Profile
398(2)
Grim Trigger
400(4)
Independent Monitoring: A Belief-Based Equilibrium for the Infinitely Repeated Prisoner's Dilemma
404(6)
A Belief-Free Example
410(5)
Almost Public Monitoring Games
415(30)
When Is Monitoring Almost Public?
415(3)
Nearby Games with Almost Public Monitoring
418(5)
Payoffs
418(1)
Continuation Values
419(2)
Best Responses
421(1)
Equilibrium
421(2)
Public Profiles with Bounded Recall
423(2)
Failure of Coordination under Unbounded Recall
425(9)
Examples
425(2)
Incentives to Deviate
427(1)
Separating Profiles
428(4)
Rich Monitoring
432(2)
Coordination Failure
434(1)
Patient Players
434(7)
Patient Strictness
435(2)
Equilibria in Nearby Games
437(4)
A Folk Theorem
441(4)
Belief-Free Equilibria in Private Monitoring Games
445(14)
Definition and Examples
445(8)
Repeated Prisoners' Dilemma with Perfect Monitoring
447(4)
Repeated Prisoners' Dilemma with Private Monitoring
451(2)
Strong Self-Generation
453(6)
Part IV Reputations
Reputations with Short-Lived Players
459(52)
The Adverse Selection Approach to Reputations
459(4)
Commitment Types
463(3)
Perfect Monitoring Games
466(12)
Building a Reputation
470(4)
The Reputation Bound
474(3)
An Example: Time Consistency
477(1)
Imperfect Monitoring Games
478(15)
Stackelberg Payoffs
480(4)
The Reputation Bound
484(8)
Small Players with Idiosyncratic Signals
492(1)
Temporary Reputations
493(7)
Asymptotic Beliefs
494(2)
Uniformly Disappearing Reputations
496(1)
Asymptotic Equilibrium Play
497(3)
Temporary Reputations: The Proof of Proposition 15.5.1
500(11)
Player 2's Posterior Beliefs
500(2)
Player 2's Beliefs about Her Future Behavior
502(1)
Player 1's Beliefs about Player 2's Future Behavior
503(6)
Proof of Proposition 15.5.1
509(2)
Reputations with Long-Lived Players
511(38)
The Basic Issue
511(4)
Perfect Monitoring and Minmax-Action Reputations
515(6)
Minmax-Action Types and Conflicting Interests
515(3)
Examples
518(2)
Two-Sided Incomplete Information
520(1)
Weaker Reputations for Any Action
521(3)
Imperfect Public Monitoring
524(7)
Commitment Types Who Punish
531(2)
Equal Discount Factors
533(14)
Example 1: Common Interests
534(3)
Example 2: Conflicting Interests
537(3)
Example 3: Strictly Dominant Action Games
540(1)
Example 4: Strictly Conflicting Interests
541(3)
Bounded Recall
544(2)
Reputations and Bargaining
546(1)
Temporary Reputations
547(2)
Finitely Repeated Games
549(18)
The Chain Store Game
550(4)
The Prisoners' Dilemma
554(6)
The Product-Choice Game
560(7)
The Last Period
562(1)
The First Period, Player 1
562(3)
The First Period, Player 2
565(2)
Modeling Reputations
567(52)
An Alternative Model of Reputations
568(8)
Modeling Reputations
568(2)
The Market
570(3)
Reputation with Replacements
573(3)
How Different Is It?
576(1)
The Role of Replacements
576(4)
Good Types and Bad Types
580(4)
Bad Types
580(1)
Good Types
581(3)
Reputations with Common Consumers
584(12)
Belief-Free Equilibria with Idiosyncratic Consumers
585(1)
Common Consumers
586(1)
Reputations
587(1)
Replacements
588(2)
Continuity at the Boundary and Markov Equilibria
590(4)
Competitive Markets
594(2)
Discrete Choices
596(3)
Lost Consumers
599(11)
The Purchase Game
599(1)
Bad Reputations: The Stage Game
600(1)
The Repeated Game
601(2)
Incomplete Information
603(4)
Good Firms
607(1)
Captive Consumers
608(2)
Markets for Reputations
610(9)
Reputations Have Value
610(3)
Buying Reputations
613(6)
Bibliography 619(10)
Symbols 629(2)
Index 631

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