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SI ES DE SU INTERES ENVIAR E-Mail: allainbgallardomartinez@gmail.com o LLamar 976964510.-
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 self-interest. 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.
About the Authors
Drew Fudenberg is Professor of Economics at MIT.
Jean Tirole is Scientific Director at the Institut d'Economie Industrielle, Researcher at CERAS (of the Ecole Nationale des Ponts et Chaussées), and Visiting Professor at the Massachusetts Institute of Technology.
INDICE
Game Theory
Drew Fudenberg and Jean Tirole
Acknowledgments xv
Introduction xvii
I Static Games of Complete Information 1
1 Games in Strategic Form and Nash Equilibrium 3
1.1 Introduction to Games in Strategic Form and Iterated Strict Dominance 4
1.2 Nash Equilibrium 11
1.3 Existence and Properties of Nash Equilibria 29
Exercises 36
References 42
2 Iterated Strict Dominance, Rationalizability, and Correlated Equilibrium 45
2.1 Iterated Strict Dominance and Rationalizability 45
2.2 Correlated Equilibrium 53
2.3 Rationalizability and Subjective Correlated Equilibria 59
II Dynamic Games of Complete Information 65
3 Extensive-Form Games 67
3.1 Introduction 67
3.2 Commitment and Perfection in Multi-Stage Games with Observed Actions 70
3.3 The Extensive Form 77
3.4 Strategies and Equilibria in Extensive-Form Games 83
3.5 Backward Induction and Subgame Perfection 92
3.6 Critiques of Backward Induction and Subgame Perfection 96
Exercises 100
References 105
4 Applications of Multi-Stage Games with Observed Actions 107
4.1 Introduction 107
4.2 The Principle of Optimality and Subgame Perfection 108
4.3 A First Look at Repeated Games 110
4.4 The Rubenstein-Stahl Bargaining Model 113
4.5 Simple Timing Games 117
4.6 Iterated Conditional Dominance and the Rubenstein Bargaining Game 128
4.7 Open-Loop and Closed-Loop Equilibria 130
4.8 Finite-Horizon and Infinite-Horizon Equilibria 134
Exercises 138
References 141
5 Repeated Games 145
5.1 Repeated Games with Observable Actions 146
5.2 Finitely Repeated Games 165
5.3 Repeated Games with Varying Opponents 168
5.4 Pareto Perfection and Renegotiation-Proofness in Repeated Games 174
5.5 Repeated Games with Imperfect Public Information 182
5.6 The Folk Theorem with Imperfect Public Information 192
5.7 Changing the Information Structure with the Time Period 197
Exercises 200
References 203
III Static Games of Incomplete Information 207
6 Bayesian Games and Bayesian Equilibrium 209
6.1 Incomplete Information 209
6.2 Example 6.1: Providing a Public Good under Incomplete Information 211
6.3 The Notions of Type and Strategy 213
6.4 Bayesian Equilibrium 215
6.5 Further Examples of Bayesian Equilibrium 215
6.6 Deletion of Strictly Dominated Strategies 226
6.7 Using Bayesian Equilibria to Justify Mixed Equilibria 230
6.8 The Distributional Approach 234
Exercises 237
References 241
7 Bayesian Games and Mechanical Design 243
7.1 Examples of Mechanical Design 246
7.2 Mechanism Design and the Revelation Principle 253
7.3 Mechanism Design with a Single Agent 258
7.4 Mechanisms with Several Agents: Feasible Allocations, Budget Balance, and Efficiency 268
7.5 Mechanism Design with Several Agents: Optimization 284
7.6 Further Topics in Mechanism Design 292
Appendix 303
Exercises 308
References 314
IV Dynamic Games of Incomplete Information 319
8 Equilibrium Refinements: Perfect Bayesian Equilibrium, Sequential Equilibrium, and Trembling-Hand Perfection 321
8.1 Introduction 321
8.2 Perfect Bayesian Equilibrium in Multi-Stage Games of Incomplete Information 324
8.3 Extensive-Form Refinements 336
8.4 Strategic-Form Refinements 350
Appendix 359
Exercises 360
References 364
9 Reputation Effects 367
9.1 Introduction 367
9.2 Games with a Single Long-Run Player 369
9.3 Games with a Many Long-Run Players 384
9.4 A Single "Big" Player against Many Simultaneous Long-Lived Opponents 389
Exercises 391
References 394
10 Sequential Bargaining under Incomplete Information 397
10.1 Introduction 397
10.2 Intertemporal Price Discrimination: The Single-Sale Model 400
10.3 Intertemporal Price Discrimination: The Rental or Repeated-Sale Model 416
10.4 Price Offers by and Informed Buyer 421
Exercises 428
References 432
V Advanced Topics 435
11 More Equilibrium Refinements: Stability, Forward Induction, and Iterated Weak Dominance 437
11.1 Strategic Stability 437
11.2 Signaling Games 446
11.3 Forward Induction, Iterated Weak Dominance, and "Burning Money" 460
11.4 Robust Predictions under Payoffs Uncertainty 467
Exercises 473
References 475
12 Advanced Topics in Strategic-Form Games 479
12.1 Generic Properties of Nash Equilibria 479
12.2 Existence of Nash Equilibrium in Games with Continuous Action Spaces and Discontinuous Payoffs 484
12.3 Supermodular Games 489
Exercises 497
References 498
13 Payoff-Relevant Strategies and Markov Equilibrium 501
13.1 Markov Equilibria in Specific Classes of Games 503
13.2 Markov Perfect Equilibrium in General Games: Definition and Properties 513
13.3 Differential Games 520
13.4 Capital-Accumulation Games 528
Exercises 536
References 537
14 Common Knowledge and Games 541
14.1 Introduction 541
14.2 Knowledge and Common Knowledge 542
14.3 Common Knowledge and Equilibrium 546
14.4 Common Knowledge, Almost Common Knowledge, and the Sensitivity of Equilibria to the Information Structure 554
Exercises 570
References 571
Index
Game Theory
Drew Fudenberg and Jean Tirole
Acknowledgments xv
Introduction xvii
I Static Games of Complete Information 1
1 Games in Strategic Form and Nash Equilibrium 3
1.1 Introduction to Games in Strategic Form and Iterated Strict Dominance 4
1.2 Nash Equilibrium 11
1.3 Existence and Properties of Nash Equilibria 29
Exercises 36
References 42
2 Iterated Strict Dominance, Rationalizability, and Correlated Equilibrium 45
2.1 Iterated Strict Dominance and Rationalizability 45
2.2 Correlated Equilibrium 53
2.3 Rationalizability and Subjective Correlated Equilibria 59
II Dynamic Games of Complete Information 65
3 Extensive-Form Games 67
3.1 Introduction 67
3.2 Commitment and Perfection in Multi-Stage Games with Observed Actions 70
3.3 The Extensive Form 77
3.4 Strategies and Equilibria in Extensive-Form Games 83
3.5 Backward Induction and Subgame Perfection 92
3.6 Critiques of Backward Induction and Subgame Perfection 96
Exercises 100
References 105
4 Applications of Multi-Stage Games with Observed Actions 107
4.1 Introduction 107
4.2 The Principle of Optimality and Subgame Perfection 108
4.3 A First Look at Repeated Games 110
4.4 The Rubenstein-Stahl Bargaining Model 113
4.5 Simple Timing Games 117
4.6 Iterated Conditional Dominance and the Rubenstein Bargaining Game 128
4.7 Open-Loop and Closed-Loop Equilibria 130
4.8 Finite-Horizon and Infinite-Horizon Equilibria 134
Exercises 138
References 141
5 Repeated Games 145
5.1 Repeated Games with Observable Actions 146
5.2 Finitely Repeated Games 165
5.3 Repeated Games with Varying Opponents 168
5.4 Pareto Perfection and Renegotiation-Proofness in Repeated Games 174
5.5 Repeated Games with Imperfect Public Information 182
5.6 The Folk Theorem with Imperfect Public Information 192
5.7 Changing the Information Structure with the Time Period 197
Exercises 200
References 203
III Static Games of Incomplete Information 207
6 Bayesian Games and Bayesian Equilibrium 209
6.1 Incomplete Information 209
6.2 Example 6.1: Providing a Public Good under Incomplete Information 211
6.3 The Notions of Type and Strategy 213
6.4 Bayesian Equilibrium 215
6.5 Further Examples of Bayesian Equilibrium 215
6.6 Deletion of Strictly Dominated Strategies 226
6.7 Using Bayesian Equilibria to Justify Mixed Equilibria 230
6.8 The Distributional Approach 234
Exercises 237
References 241
7 Bayesian Games and Mechanical Design 243
7.1 Examples of Mechanical Design 246
7.2 Mechanism Design and the Revelation Principle 253
7.3 Mechanism Design with a Single Agent 258
7.4 Mechanisms with Several Agents: Feasible Allocations, Budget Balance, and Efficiency 268
7.5 Mechanism Design with Several Agents: Optimization 284
7.6 Further Topics in Mechanism Design 292
Appendix 303
Exercises 308
References 314
IV Dynamic Games of Incomplete Information 319
8 Equilibrium Refinements: Perfect Bayesian Equilibrium, Sequential Equilibrium, and Trembling-Hand Perfection 321
8.1 Introduction 321
8.2 Perfect Bayesian Equilibrium in Multi-Stage Games of Incomplete Information 324
8.3 Extensive-Form Refinements 336
8.4 Strategic-Form Refinements 350
Appendix 359
Exercises 360
References 364
9 Reputation Effects 367
9.1 Introduction 367
9.2 Games with a Single Long-Run Player 369
9.3 Games with a Many Long-Run Players 384
9.4 A Single "Big" Player against Many Simultaneous Long-Lived Opponents 389
Exercises 391
References 394
10 Sequential Bargaining under Incomplete Information 397
10.1 Introduction 397
10.2 Intertemporal Price Discrimination: The Single-Sale Model 400
10.3 Intertemporal Price Discrimination: The Rental or Repeated-Sale Model 416
10.4 Price Offers by and Informed Buyer 421
Exercises 428
References 432
V Advanced Topics 435
11 More Equilibrium Refinements: Stability, Forward Induction, and Iterated Weak Dominance 437
11.1 Strategic Stability 437
11.2 Signaling Games 446
11.3 Forward Induction, Iterated Weak Dominance, and "Burning Money" 460
11.4 Robust Predictions under Payoffs Uncertainty 467
Exercises 473
References 475
12 Advanced Topics in Strategic-Form Games 479
12.1 Generic Properties of Nash Equilibria 479
12.2 Existence of Nash Equilibrium in Games with Continuous Action Spaces and Discontinuous Payoffs 484
12.3 Supermodular Games 489
Exercises 497
References 498
13 Payoff-Relevant Strategies and Markov Equilibrium 501
13.1 Markov Equilibria in Specific Classes of Games 503
13.2 Markov Perfect Equilibrium in General Games: Definition and Properties 513
13.3 Differential Games 520
13.4 Capital-Accumulation Games 528
Exercises 536
References 537
14 Common Knowledge and Games 541
14.1 Introduction 541
14.2 Knowledge and Common Knowledge 542
14.3 Common Knowledge and Equilibrium 546
14.4 Common Knowledge, Almost Common Knowledge, and the Sensitivity of Equilibria to the Information Structure 554
Exercises 570
References 571
Index
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