Repeated Games with Incomplete Information

Front Cover
Winner, Frederick W. Lanchester Prize given by The Institute for Operations Research and the Management Sciences (INFORMS), 1995.

During the height of the Cold War, between 1965 and 1968, Robert Aumann, Michael Maschler, and Richard Stearns collaborated on research on the dynamics of arms control negotiations that has since become foundational to work on repeated games. These five seminal papers are collected here for the first time, with the addition of "postscripts" describing many of the developments since the papers were written. The basic model studied throughout the book is one in which players ignorant about the game being played must learn what they can from the actions of the others.

The original work, done under contract to the United States Arms Control and Disarmament Agency, was intended to tackle the gradual disarmament problem, in which neither player knew what his own payoff would be for any given agreement, because of uncertainty about the other side's arsenal and weapons production technology. But the research soon became much more generalized, covering information concealment and revelation, signaling and learning, and related ideas in any repeated competitive situation.

The first four chapters of the book treat the competitive zero-sum side of the theory of repeated games. Chapter five takes up cooperative phenomena where one player may want to signal information to another. An extensive bibliography covers all items mentioned in the main text, in the postscripts, and in the introduction. The bibliography also includes a compilation of published papers and books that refer to the original reports.
 

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Contents

A Case When a Player Should Disclose
10
Conclusions
38
Optimal Strategies of the Uninformed
53
Repeated Games and the Problem
66
Lack of Information on One SideStage Games
70
Lack of Information on Both Sides
91
Incomplete Knowledge of Moves
110
Further Problems
129
Games Without a Recursive Structure
219
Equilibrium Points and Equilibrium Payoffs
226
Equilibrium Payoffs of
233
Repeated Games with Incomplete
240
The Possibility of Cheating
257
More Equilibrium Points
269
More Equilibrium Payoffs
277
Postscripts
294

Chapter Four
173
Examples
181
The Value
188
Postscripts
206
Optimal Strategies for the Uninformed
212
g An Economic Example Requiring
311
h Known Own Payoffs
320
Index
335
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