Repeated Games with Incomplete Information
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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A Case When a Player Should Disclose
Optimal Strategies of the Uninformed
Repeated Games and the Problem
Lack of Information on One SideStage Games
Lack of Information on Both Sides
Incomplete Knowledge of Moves
Games Without a Recursive Structure
Equilibrium Points and Equilibrium Payoffs
Equilibrium Payoffs of
Repeated Games with Incomplete
The Possibility of Cheating
More Equilibrium Points
More Equilibrium Payoffs
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actions actually alternatives approachable assigns assume called cav u(p Chapter choice of chance chooses chosen column communication complete compute conditional probability consider convex course defined definition denote depend described determined deviation discussed equal equilibrium payoffs error term example exists expected payoff expression fact Figure finite follows formal function gain given guarantee implies incomplete information independent infinite knowledge known leads least limit lottery matrix means mixed moves Note observing obtain optimal strategy original outcome pair play Player Player 1's positive possible Postscript precisely probability distribution proof prove pure remains repeated game represents respectively result reveal rules sequence side signal situation stage game Step strategy for Player Suppose Theorem theory tion treated vector yields