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Preface xi
1 Decision-Theoretic Foundations 1 (36)
1.1 Game Theory, Rationality, and 1 (4)
Intelligence
1.2 Basic Concepts of Decision Theory 5 (4)
1.3 Axioms 9 (3)
1.4 The Expected-Utility Maximization 12 (6)
Theorem
1.5 Equivalent Representations 18 (3)
1.6 Bayesian Conditional-Probability 21 (1)
Systems
1.7 Limitations of the Bayesian Model 22 (4)
1.8 Domination 26 (5)
1.9 Proofs of the Domination Theorems 31 (2)
Exercises 33 (4)
2 Basic Models 37 (51)
2.1 Games in Extensive Form 37 (9)
2.2 Strategic Form and the Normal 46 (5)
Representation
2.3 Equivalence of Strategic-Form Games 51 (3)
2.4 Reduced Normal Representations 54 (3)
2.5 Elimination of Dominated Strategies 57 (4)
2.6 Multiagent Representations 61 (2)
2.7 Common Knowledge 63 (4)
2.8 Bayesian Games 67 (7)
2.9 Modeling Games with Incomplete 74 (9)
Information
Exercises 83 (5)
3 Equilibria of Strategic-Form Games 88 (66)
3.1 Domination and Rationalizability 88 (3)
3.2 Nash Equilibrium 91 (8)
3.3 Computing Nash Equilibria 99 (6)
3.4 Significance of Nash Equilibria 105(3)
3.5 The Focal-Point Effect 108(6)
3.6 The Decision-Analytic Approach to Games 114(3)
3.7 Evolution, Resistance, and Risk 117(5)
Dominance
3.8 Two-Person Zero-Sum Games 122(5)
3.9 Bayesian Equilibria 127(2)
3.10 Purification of Randomized Strategies 129(3)
in Equilibria
3.11 Auctions 132(4)
3.12 Proof of Existence of Equilibrium 136(4)
3.13 Infinite Strategy Sets 140(8)
Exercises 148(6)
4 Sequential Equilibria of Extensive-Form 154(59)
Games
4.1 Mixed Strategies and Behavioral 154(7)
Strategies
4.2 Equilibria in Behavioral Strategies 161(2)
4.3 Sequential Rationality at Information 163(5)
States with Positive Probability
4.4 Consistent Beliefs and Sequential 168(9)
Rationality at All Information States
4.5 Computing Sequential Equilibria 177(6)
4.6 Subgame-Perfect Equilibria 183(2)
4.7 Games with Perfect Information 185(2)
4.8 Adding Chance Events with Small 187(3)
Probability
4.9 Forward Induction 190(6)
4.10 Voting and Binary Agendas 196(6)
4.11 Technical Proofs 202(6)
Exercises 208(5)
5 Refinements of Equilibrium in Strategic 213(31)
Form
5.1 Introduction 213(3)
5.2 Perfect Equilibria 216(5)
5.3 Existence of Perfect and Sequential 221(1)
Equilibria
5.4 Proper Equilibria 222(8)
5.5 Persistent Equilibria 230(2)
5.6 Stable Sets of Equilibria 232(7)
5.7 Generic Properties 239(1)
5.8 Conclusions 240(2)
Exercises 242(2)
6 Games with Communication 244(64)
6.1 Contracts and Correlated Strategies 244(5)
6.2 Correlated Equilibria 249(9)
6.3 Bayesian Games with Communication 258(5)
6.4 Bayesian Collective-Choice Problems 263(8)
and Bayesian Bargaining Problems
6.5 Trading Problems with Linear Utility 271(10)
6.6 General Participation Constraints for 281(2)
Bayesian Games with Contracts
6.7 Sender-Receiver Games 283(5)
6.8 Acceptable and Predominant Correlated 288(6)
Equilibria
6.9 Communication in Extensive-Form and 294(5)
Multistage Games
Exercises 299(8)
Bibliographic Note 307(1)
7 Repeated Games 308(62)
7.1 The Repeated Prisoners' Dilemma 308(2)
7.2 A General Model of Repeated Games 310(7)
7.3 Stationary Equilibria of Repeated 317(6)
Games with Complete State Information and
Discounting
7.4 Repeated Games with Standard 323(8)
Information: Examples
7.5 General Feasibility Theorems for 331(6)
Standard Repeated Games
7.6 Finitely Repeated Games and the Role 337(5)
of Initial Doubt
7.7 Imperfect Observability of Moves 342(7)
7.8 Repeated Games in Large Decentralized 349(3)
Groups
7.9 Repeated Games with Incomplete 352(9)
Information
7.10 Continuous Time 361(3)
7.11 Evolutionary Simulation of Repeated 364(1)
Games
Exercises 365(5)
8 Bargaining and Cooperation in Two-Person 370(47)
Games
8.1 Noncooperative Foundations of 370(5)
Cooperative Game Theory
8.2 Two-Person Bargaining Problems and the 375(6)
Nash Bargaining Solution
8.3 Interpersonal Comparisons of Weighted 381(3)
Utility
8.4 Transferable Utility 384(1)
8.5 Rational Threats 385(5)
8.6 Other Bargaining Solutions 390(4)
8.7 An Alternating-Offer Bargaining Game 394(5)
8.8 An Alternating-Offer Game with 399(4)
Incomplete Information
8.9 A Discrete Alternating-Offer Game 403(5)
8.10 Renegotiation 408(4)
Exercises 412(5)
9 Coalitions in Cooperative Games 417(66)
9.1 Introduction to Coalitional Analysis 417(5)
9.2 Characteristic Functions with 422(5)
Transferable Utility
9.3 The Core 427(9)
9.4 The Shapley Value 436(8)
9.5 Values with Cooperation Structures 444(8)
9.6 Other Solution Concepts 452(4)
9.7 Coalitional Games with Nontransferable 456(6)
Utility
9.8 Cores without Transferable Utility 462(6)
9.9 Values without Transferable Utility 468(10)
Exercises 478(3)
Bibliographic Note 481(2)
10 Cooperation under Uncertainty 483(56)
10.1 Introduction 483(2)
10.2 Concepts of Efficiency 485(4)
10.3 An Example 489(4)
10.4 Ex Post Inefficiency and Subsequent 493(4)
Offers
10.5 Computing Incentive-Efficient 497(5)
Mechanisms
10.6 Inscrutability and Durability 502(7)
10.7 Mechanism Selection by an Informed 509(6)
Principal
10.8 Neutral Bargaining Solutions 515(11)
10.9 Dynamic Matching Processes with 526(8)
Incomplete Information
Exercises 534(5)
Bibliography 539(14)
Index 553