Game Theory

by Fudenberg, Drew; Tirole, Jean

• ISBN13: 9780262061414
• ISBN10: 0262061414
• Format: Hardcover
• Copyright: 1991-08-29
• Publisher: The MIT Press

Summary

This advanced text introduces the principles of noncooperative game theory - including strategic form games, Nash equilibria, subgame perfection, repeated games, and games of incomplete information - in a direct and uncomplicated style that will acquaint students with the broad spectrum of the field while highlighting and explaining what they need to know at any given point. The analytic material is accompanied by many applications, examples, and exercises. The theory of noncooperative games studies the behavior of agents in any situation where each agent's optimal choice may depend on a forecast of the opponents' choices. "Noncooperative" refers to choices that are based on the participant's perceived selfinterest. Although game theory has been applied to many fields, Fudenberg and Tirole focus on the kinds of game theory that have been most useful in the study of economic problems. They also include some applications to political science. The fourteen chapters are grouped in parts that cover static games of complete information, dynamic games of complete information, static games of incomplete information, dynamic games of incomplete information, and advanced topics. Drew Fudenberg and Jean Tirole are Professors of Economics at MIT.

Author Biography

Drew Fudenberg is Professor of Economics at MIT.

Jean Tirole, the 2014 Nobel Laureate in Economics, is Scientific Director of IDEI (Institut d'Economie Industrielle), Chairman of the Board of TSE (Toulouse School of Economics), and Annual Visiting Professor of Economics at MIT.

Table of Contents

Acknowledgments	xv
Introduction	xvii
I Static Games of Complete Information	1	(64)
Games in Strategic Form and Nash Equilibrium	3	(42)
Introduction to Games in Strategic Form and Iterated Strict Dominance	4	(7)
Strategic-Form Games	4	(2)
Dominated Strategies	6	(3)
Applications of the Elimination of Dominated Strategies	9	(2)
Nash Equilibrium	11	(18)
Definition of Nash Equilibrium	11	(3)
Examples of Pure-Strategy Equilibria	14	(2)
Nonexistence of a Pure-Strategy Equilibrium	16	(2)
Multiple Nash Equilibria, Focal Points, and Pareto Optimality	18	(5)
Nash Equilibrium as the Result of Learning or Evolution	23	(6)
Existence and Properties of Nash Equilibria	29	(16)
Existence of a Mixed-Strategy Equilibrium	29	(1)
The Nash-Equilibrium Correspondence Has a Closed Graph	30	(4)
Existence of Nash Equilibrium in Infinite Games with Continuous Payoffs	34	(2)
Exercises	36	(6)
References	42	(3)
Iterated Strict Dominance, Rationalizability, and Correlated Equilibrium	45	(20)
Iterated Strict Dominance and Rationalizability	45	(8)
Iterated Strict Dominance: Definition and Properties	45	(2)
An Application of Iterated Strict Dominance	47	(1)
Rationalizability	48	(2)
Rationalizability and Iterated Strict Dominance	50	(3)
Discussion	53	(1)
Correlated Equilibrium	53	(6)
Rationalizability and Subjective Correlated Equilibria	59	(6)
Exercises	60	(3)
References	63	(2)
II Dynamic Games of Complete Information	65	(142)
Extensive-Form Games	67	(40)
Introduction	67	(3)
Commitment and Perfection in Multi-Stage Games with Observed Actions	70	(7)
What Is a Multi-Stage Game?	70	(2)
Backward Induction and Subgame Perfection	72	(2)
The Value of Commitment and ``Time Consistency''	74	(3)
The Extensive Form	77	(6)
Definition	77	(5)
Multi-Stage Games with Observed Actions	82	(1)
Strategies and Equilibria in Extensive-Form Games	83	(9)
Behavior Strategies	83	(2)
The Strategic-Form Representation of Extensive-Form Games	85	(2)
The Equivalence between Mixed and Behavior Strategies in Games of Perfect Recall	87	(3)
Iterated Strict Dominance and Nash Equilibrium	90	(2)
Backward Induction and Subgame Perfection	92	(4)
Critiques of Backward Induction and Subgame Perfection	96	(11)
Critiques of Backward Induction	97	(2)
Critiques of Subgame Perfection	99	(1)
Exercises	100	(5)
References	105	(2)
Applications of Multi-Stage Games with Observed Actions	107	(38)
Introduction	107	(1)
The Principle of Optimality and Subgame Perfection	108	(2)
A First Look at Repeated Games	110	(3)
The Repeated Prisoner's Dilemma	110	(2)
A Finitely Repeated Game with Several Static Equilibria	112	(1)
The Rubinstein-Stahl Bargaining Model	113	(4)
A Subgame-Perfect Equilibrium	113	(2)
Uniqueness of the Infinite-Horizon Equilibrium	115	(1)
Comparative Statics	116	(1)
Simple Timing Games	117	(11)
Definition of Simple Timing Games	117	(3)
The War of Attrition	120	(6)
Preemption Games	126	(2)
Iterated Conditional Dominance and the Rubinstein Bargaining Game	128	(2)
Open-Loop and Closed-Loop Equilibria	130	(4)
Definitions	130	(2)
A Two-Period Example	132	(1)
Open-Loop and Closed-Loop Equilibria in Games with Many Players	133	(1)
Finite-Horizon and Infinite-Horizon Equilibria	134	(11)
Exercises	138	(3)
References	141	(4)
Repeated Games	145	(62)
Repeated Games with Observable Actions	146	(19)
The Model	146	(4)
The Folk Theorem for Infinitely Repeated Games	150	(10)
Characterization of the Equilibrium Set	160	(5)
Finitely Repeated Games	165	(3)
Repeated Games with Varying Opponents	168	(6)
Repeated Games with Long-Run and Short-Run Players	168	(3)
Games with Overlapping Generations of Players	171	(1)
Randomly Matched Opponents	172	(2)
Pareto Perfection and Renegotiation-Proofness in Repeated Games	174	(8)
Introduction	174	(2)
Pareto Perfection in Finitely Repeated Games	176	(3)
Renegotiation-Proofness in Infinitely Repeated Games	179	(3)
Repeated Games with Imperfect Public Information	182	(10)
The Model	183	(2)
Trigger-Price Strategies	185	(2)
Public Strategies and Public Equilibria	187	(1)
Dynamic Programming and Self-Generation	188	(4)
The Folk Theorem with Imperfect Public Information	192	(5)
Changing the Information Structure with the Time Period	197	(10)
Exercises	200	(3)
References	203	(4)
III Static Games of Incomplete Information	207	(112)
Bayesian Games and Bayesian Equilibrium	209	(34)
Incomplete Information	209	(2)
Example 6.1: Providing a Public Good under Incomplete Information	211	(2)
The Notions of Type and Strategy	213	(2)
Bayesian Equilibrium	215	(1)
Further Examples of Bayesian Equilibria	215	(11)
Deletion of Strictly Dominated Strategies	226	(4)
Interim vs. Ex Ante Dominance	226	(2)
Examples of Iterated Strict Dominance	228	(2)
Using Bayesian Equilibria to Justify Mixed Equilibria	230	(4)
Examples	230	(3)
Purification Theorem	233	(1)
The Distributional Approach	234	(9)
Exercises	237	(4)
References	241	(2)
Bayesian Games and Mechanism Design	243	(76)
Examples of Mechanism Design	246	(7)
Nonlinear Pricing	246	(4)
Auctions	250	(3)
Mechanism Design and the Revelation Principle	253	(5)
Mechanism Design with a Single Agent	258	(10)
Implementable Decisions and Allocations	258	(4)
Optimal Mechanisms	262	(6)
Mechanisms with Several Agents: Feasible Allocations, Budget Balance, and Efficiency	268	(16)
Feasibility under Budget Balance	269	(1)
Dominant Strategy vs. Bayesian Mechanisms	270	(1)
Efficiency Theorems	271	(4)
Inefficiency Theorems	275	(4)
Efficiency Limit Theorems	279	(2)
Strong Inefficiency Limit Theorems	281	(3)
Mechanism Design with Several Agents: Optimization	284	(8)
Auctions	284	(4)
Efficient Bargaining Processes	288	(4)
Further Topics in Mechanism Design	292	(27)
Correlated Types	292	(3)
Risk Aversion	295	(2)
Informed Principal	297	(2)
Dynamic Mechanism Design	299	(2)
Common Agency	301	(2)
Appendix	303	(5)
Exercises	308	(6)
References	314	(5)
IV Dynamic Games of Incomplete Information	319	(116)
Equilibrium Refinements: Perfect Bayesian Equilibrium, Sequential Equilibrium, and Trembling-Hand Perfection	321	(46)
Introduction	321	(3)
Perfect Bayesian Equilibrium in Multi-Stage Games of Incomplete Information	324	(12)
The Basic Signaling Game	324	(2)
Examples of Signaling Games	326	(5)
Multi-Stage Games with Observed Actions and Incomplete Information	331	(5)
Extensive-Form Refinements	336	(14)
Review of Game Trees	336	(1)
Sequential Equilibrium	337	(4)
Properties of Sequential Equilibrium	341	(4)
Sequential Equilibrium Compared with Perfect Bayesian Equilibrium	345	(5)
Strategic-Form Refinements	350	(17)
Trembling-Hand Perfect Equilibrium	351	(5)
Proper Equilibrium	356	(3)
Appendix	359	(1)
Exercises	360	(4)
References	364	(3)
Reputation Effects	367	(30)
Introduction	367	(2)
Games with a Single Long-Run Player	369	(15)
The Chain-Store Game	369	(5)
Reputation Effects with a Single Long-Run Player: The General Case	374	(7)
Extensive-Form Stage Games	381	(3)
Games with Many Long-Run Players	384	(5)
General Stage Games and General Reputations	384	(2)
Common-Interest Games and Bounded-Recall Reputations	386	(3)
A Single ``Big'' Player against Many Simultaneous Long-Lived Opponents	389	(8)
Exercises	391	(3)
References	394	(3)
Sequential Bargaining under Incomplete Information	397	(38)
Introduction	397	(3)
Intertemporal Price Discrimination: The Single-Sale Model	400	(16)
The Framework	400	(2)
A Two-Period Introduction to Coasian Dynamics	402	(3)
An Infinite-Horizon Example of the Coase Conjecture	405	(1)
The Skimming Property	406	(2)
The Gap Case	408	(3)
The No-Gap Case	411	(3)
Gap vs. No Gap and Extensions of the Single-Sale Model	414	(2)
Intertemporal Price Discrimination: The Rental or Repeated-Sale Model	416	(5)
Short-Term Contracts	417	(2)
Long-Term Contracts and Renegotiation	419	(2)
Price Offers by an Informed Buyer	421	(14)
One-Sided Offers and Bilateral Asymmetric Information	422	(2)
Alternating Offers and One-Sided Asymmetric Information	424	(3)
Mechanism Design and Bargaining	427	(1)
Exercises	428	(4)
References	432	(3)
V Advanced Topics	435	(138)
More Equilibrium Refinements: Stability, Forward Induction, and Iterated Weak Dominance	437	(42)
Strategic Stability	437	(9)
Signaling Games	446	(14)
Forward Induction, Iterated Weak Dominance, and ``Burning Money''	460	(7)
Robust Predictions under Payoff Uncertainty	467	(12)
Exercises	473	(2)
References	475	(4)
Advanced Topics in Strategic-Form Games	479	(22)
Generic Properties of Nash Equilibria	479	(5)
Number of Nash Equilibria	479	(1)
Robustness of Equilibria to Payoff Perturbations	480	(4)
Existence of Nash Equilibrium in Games with Continuous Action Spaces and Discontinuous Payoffs	484	(5)
Existence of a Pure-Strategy Equilibrium	485	(2)
Existence of a Mixed-Strategy Equilibrium	487	(2)
Supermodular Games	489	(12)
Exercises	497	(1)
References	498	(3)
Payoff-Relevant Strategies and Markov Equilibrium	501	(40)
Markov Equilibria in Specific Classes of Games	503	(10)
Stochastic Games: Definition and Existence of MPE	503	(2)
Separable Sequential Games	505	(2)
Examples from Economics	507	(6)
Markov Perfect Equilibrium in General Games: Definition and Properties	513	(7)
Definition	513	(2)
Existence	515	(3)
Robustness to Payoff Perturbations	518	(2)
Differential Games	520	(8)
Definition	520	(1)
Equilibrium Conditions	521	(2)
Linear-Quadratic Differential Games	523	(2)
Technical Issues	525	(2)
Zero-Sum Differential Games	527	(1)
Capital-Accumulation Games	528	(13)
Open-Loop, Closed-Loop, and Markov Strategies	529	(5)
Differential-Game Strategies	534	(2)
Exercises	536	(1)
References	537	(4)
Common Knowledge and Games	541	(32)
Introduction	541	(1)
Knowledge and Common Knowledge	542	(4)
Common Knowledge and Equilibrium	546	(8)
The Dirty Faces and the Sage	547	(1)
Agreeing to Disagree	548	(2)
No-Speculation Theorems	550	(4)
Interim Efficiency and Incomplete Contracts	554	(1)
Common Knowledge, Almost Common Knowledge, and the Sensitivity of Equilibria to the Information Structure	554	(19)
The Lack of Lower Hemi-Continuity	556	(6)
Lower Hemi-Continuity and Almost Common Knowledge	562	(8)
Exercises	570	(1)
References	571	(2)
Index	573