## Repeated Games with Incomplete InformationWinner, 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 |

### Other editions - View all

Repeated Games with Incomplete Information Robert J. Aumann,Michael Maschler No preview available - 1995 |

### Common terms and phrases

1-shot game Ai(p assume average expected payoff average payoff cav u(p cav vex chance chooses chance's choice Chapter choice of chance chooses left chosen column compute concave concave function conditional probability convex convex hull defined denote deviation Dick diconvex equilibrium pair equilibrium payoffs error term example exists Figure finite follows function game AI game theory game with incomplete guarantee Harsanyi incomplete information joint plan know the choice Lemma lim vn martingale matrix minimax theorem mixed strategy n-stage optimal strategy outcome pair of strategies payoff matrix payoff to Player payoff vector Player 1 chooses Player 1 plays Player 2 knows playing optimally positive probability Postscript prisoner's dilemma probability 1/2 probability distribution probability vector proof pure strategy random variable repeated game result reveal Section sequence situation strategy for Player Theorem Nl tion true game true stage game vector payoff yields Zamir