Repeated Games with Incomplete Information Book

	Preface
Ch. 1	Game Theoretic Aspects of Gradual Disarmament
2	A Case When a Player Cannot Benefit in the Long Run from His Information	3
3	A Case When a Player Should Disclose His Information	10
4	A Case When a Player Should Partially Disclose His Information	11
5	The Main Theorem	22
6	The Optimal Strategy of Player 2	34
7	Conclusions
8	Where Do We Go From Here?	39
	Postscript a Martingales	42
	Postscript b Convexity and Concavity as Monotonicity in Information	43
	Postscript c The Error Term	44
	Postscript d Optimal Strategies of the Uninformed Player	53
	Postscript e Monotonicity of v[subscript n] and the Recursive Structure of [actual symbol not reproducible]	61
Ch. 2	Repeated Games with Incomplete Information: A Survey of Recent Results
2	Repeated Games and the Problem of Information	66
3	Lack of Information on One Side - Stage Games in Normal Form	70
4	Lack of Information on Both Sides	91
5	Incomplete Knowledge of Moves	110
6	Further Problems
	Postscript a Incomplete Information on Both Sides: lim v[subscript n]	130
	Postscript b Incomplete Information on Both Sides: The Limit of the Discounted Values	130
	Postscript c The Conceptual Distinction Between [actual symbol not reproducible]: Generalities	131
	Postscript d The Conceptual Distinction Between [actual symbol not reproducible]: Incomplete Information	136
	Postscript e Non-Zero Sum Games	137
	Postscript f Discounting	139
	Postscript g Continuous Time	140
	Postscript h Alternative Definitions of Value, Maxmin, and Minmax in [actual symbol not reproducible]	140
	Postscript i Incomplete Information on Both Sides: The Dependent Case	143
	Postscript j Incomplete Information on One-and-a-Half Sides	145
Ch. 3	A Formal Information Concept for Games with Incomplete Information	155
Ch. 4	Repeated Games of Incomplete Information: The Zero-Sum Extensive Case
2	Motivation	176
3	The Mathematical Model	177
4	Examples	181
5	The Infinite-Stage Game and its Relation to the n-Stage Games	186
6	Statement of the Main Theorem: The Value of the Infinite-Stage Game	188
7	Proof of the Main Theorem	191
	Postscript a Monotonicity of v[subscript n] and the Informed Player's Information Matrices	206
	Postscript b Remembering One's Own Moves	211
	Postscript c Optimal Strategies for the Uninformed Player	212
	Postscript d The Case When P2 Knows His Payoff	212
	Postscript e The Error Term	213
	Postscript f Incomplete Information on Both Sides	215
	Postscript g Both Players Have Incomplete Information and Know Their Own Payoffs	216
	Postscript h Identical Information	216
	Postscript i Games Without a Recursive Structure	219
Ch. 5	Repeated Games of Incomplete Information: An Approach to the Non-Zero-Sum Case
2	Equilibrium Points and Equilibrium Payoffs in a 2-Player One-Shot Game	226
3	Equilibrium Payoffs of an Infinitely-Repeated 2-Player Game with Complete Information	233
4	Repeated Games with Incomplete Information	240
5	The Possibility of Cheating	257
6	Joint Plans	260
7	More Equilibrium Points	269
8	More Equilibrium Payoffs	277
	Postscript a Existence of Equilibria	294
	Postscript b The Folk Theorem and Individual Rationality	294
	Postscript c Characterization of Equilibria: Background	294
	Postscript d Characterization of Equilibria: Geometric Preliminaries	296
	Postscript e Characterization of Equilibria: Precise Formulation	298
	Postscript f Characterization of Equilibria: Outline of Hart's Proof	301
	Postscript g An Economic Example Requiring Unboundedly Many Communications	311
	Postscript h Known Own Payoffs	320
	Postscript i Communication Equilibria	320
	Postscript j Perturbations	321
	Bibliography	323
	Index	335