A course in game theory  by Martin J. Osborne and Ariel Rubinstein

Table of contents

	Preface xi
1	Introduction   1
	1.1	Game Theory   1
	1.2	Games and Solutions   2
	1.3	Game Theory and the Theory of Competitive Equilibrium   3
	1.4	Rational Behavior   4
	1.5	The Steady State and Deductive Interpretations   5
	1.6	Bounded Rationality   6
	1.7	Terminology and Notation   6
		Notes   8
I	Strategic Games   9
2	Nash Equilibrium   11
	2.1	Strategic Games   11
	2.2	Nash Equilibrium   14
	2.3	Examples   15
	2.4	Existence of a Nash Equilibrium   19
	2.5	Strictly Competitive Games   21
	2.6	Bayesian Games: Strategic Games with Imperfect Information   24
		Notes   29
3	Mixed, Correlated, and Evolutionary Equilibrium   31
	3.1	Mixed Strategy Nash Equilibrium   31
	3.2	Interpretations of Mixed Strategy Nash Equilibrium   37
	3.3	Correlated Equilibrium   44
	3.4	Evolutionary Equilibrium   48
		Notes   51
4	Rationalizability and Iterated Elimination of Dominated Actions   53
	4.1	Rationalizability   53
	4.2	Iterated Elimination of Strictly Dominated Actions   58
	4.3	Iterated Elimination of Weakly Dominated Actions   62
		Notes   64
5	Knowledge and Equilibrium   67
	5.1	A Model of Knowledge   67
	5.2	Common Knowledge   73
	5.3	Can People Agree to Disagree?   75
	5.4	Knowledge and Solution Concepts   76
	5.5	The Electronic Mail Game   81
		Notes   84
II	Extensive Games with Perfect Information   87
6	Extensive Games with Perfect Information   89
	6.1	Extensive Games with Perfect Information   89
	6.2	Subgame Perfect Equilibrium   97
	6.3	Two Extensions of the Definition of a Game   101
	6.4	The Interpretation of a Strategy   103
	6.5	Two Notable Finite Horizon Games   105
	6.6	Iterated Elimination of Weakly Dominated Strategies   108
		Notes   114
7	Bargaining Games   117
	7.1	Bargaining and Game Theory   117
	7.2	A Bargaining Game of Alternating Offers   118
	7.3	Subgame Perfect Equilibrium   121
	7.4	Variations and Extensions   127
		Notes   131
8	Repeated Games   133
	8.1	The Basic Idea   133
	8.2	Infinitely Repeated Games vs.\ Finitely Repeated Games   134
	8.3	Infinitely Repeated Games: Definitions   136
	8.4	Strategies as Machines   140
	8.5	Trigger Strategies: Nash Folk Theorems   143
	8.6	Punishing for a Limited Length of Time: A Perfect Folk Theorem for the Limit of Means Criterion   146
	8.7	Punishing the Punisher: A Perfect Folk Theorem for the Overtaking Criterion   149
	8.8	Rewarding Players Who Punish: A Perfect Folk Theorem for the Discounting Criterion   150
	8.9	The Structure of Subgame Perfect Equilibria Under the Discounting Criterion   153
	8.10	Finitely Repeated Games   155
		Notes   160
9	Complexity Considerations in Repeated Games   163
	9.1	Introduction   163
	9.2	Complexity and the Machine Game   164
	9.3	The Structure of the Equilibria of a Machine Game   168
	9.4	The Case of Lexicographic Preferences   172
		Notes   175
10	Implementation Theory   177
	10.1	Introduction   177
	10.2	The Implementation Problem   178
	10.3	Implementation in Dominant Strategies   180
	10.4	Nash Implementation   185
	10.5	Subgame Perfect Equilibrium Implementation   191
		Notes   195
III	Extensive Games with Imperfect Information   197
11	Extensive Games with Imperfect Information   199
	11.1	Extensive Games with Imperfect Information   199
	11.2	Principles for the Equivalence of Extensive Games   204
	11.3	Framing Effects and the Equivalence of Extensive Games   209
	11.4	Mixed and Behavioral Strategies   212
	11.5	Nash Equilibrium   216
		Notes   217
12	Sequential Equilibrium   219
	12.1	Strategies and Beliefs   219
	12.2	Sequential Equilibrium   222
	12.3	Games with Observable Actions: Perfect Bayesian Equilibrium   231
	12.4	Refinements of Sequential Equilibrium   243
	12.5	Trembling Hand Perfect Equilibrium   246
		Notes   254
IV	Coalitional Games   255
13	The Core   257
	13.1	Coalitional Games with Transferable Payoff   257
	13.2	The Core   258
	13.3	Nonemptiness of the Core   262
	13.4	Markets with Transferable Payoff   263
	13.5	Coalitional Games without Transferable Payoff   268
	13.6	Exchange Economies   269
		Notes   274
14	Stable Sets, the Bargaining Set, and the Shapley Value   277
	14.1	Two Approaches   277
	14.2	The Stable Sets of von Neumann and Morgenstern   278
	14.3	The Bargaining Set, Kernel, and Nucleolus   281
	14.4	The Shapley Value   289
		Notes   297
15	The Nash Solution   299
	15.1	Bargaining Problems   299
	15.2	The Nash Solution: Definition and Characterization   301
	15.3	An Axiomatic Definition   305
	15.4	The Nash Solution and the Bargaining Game of Alternating Offers   310
	15.5	An Exact Implementation of the Nash Solution   311
		Notes   312
	List of Results   313
	References   321
	Index   341