## Stochastic Games and ApplicationsThis volume is based on lectures given at the NATO Advanced Study Institute on "Stochastic Games and Applications," which took place at Stony Brook, NY, USA, July 1999. It gives the editors great pleasure to present it on the occasion of L.S. Shapley's eightieth birthday, and on the fiftieth "birthday" of his seminal paper "Stochastic Games," with which this volume opens. We wish to thank NATO for the grant that made the Institute and this volume possible, and the Center for Game Theory in Economics of the State University of New York at Stony Brook for hosting this event. We also wish to thank the Hebrew University of Jerusalem, Israel, for providing continuing financial support, without which this project would never have been completed. In particular, we are grateful to our editorial assistant Mike Borns, whose work has been indispensable. We also would like to acknowledge the support of the Ecole Poly tech nique, Paris, and the Israel Science Foundation. March 2003 Abraham Neyman and Sylvain Sorin ix STOCHASTIC GAMES L.S. SHAPLEY University of California at Los Angeles Los Angeles, USA 1. Introduction In a stochastic game the play proceeds by steps from position to position, according to transition probabilities controlled jointly by the two players. |

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### Contents

15 | |

S Stochastic games Chapter 1 pp 17 | 25 |

Neyman A Real algebraic tools in stochastic games Chapter 6 pp 5775 | 57 |

Nowak A S Zerosum stochastic games with borel state spaces Chapter | 82 |

Solan E Perturbations of Markov chains with applications to stochastic | 265 |

Sorin S Symmetric incomplete information games as stochastic games | 323 |

Maitra A and Sudderth W Stochastic Games with lim sup Payoff Chap | 355 |

Sorin S The operator approach to zerosum stochastic games Chapter | 415 |

The latticetheoretic approach | 443 |

Contributors pp 471473 | 471 |

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a-field absorbing game algorithm analytic sets assume assumptions behavioral strategies Borel measurable Borel set compact continuous converges convex Corollary correlated equilibrium corresponding countable defined denote discounted stochastic games Dordrecht equilibrium payoff exists exit distribution finite follows function f Game Theory Games and Applications games with absorbing given graph hence implies induction inequality initial integer Journal of Game Kluwer Academic Publishers Lemma limiting average Mathematics of Operations maxmin measurable functions measurable map minmax mixed action mixed strategy Nash equilibrium Neyman non-absorbing non-zero-sum nonexpansive optimal strategies orderfield property payoff function perfect information Physical Sciences play probability measure proof Proposition prove Puiseux pure strategy Raghavan recursive games repeated games resp satisfies Science Series Section semialgebraic set sequence Shapley signal Sn(w Sorin eds stage stochastic games strategy G strategy of player subset Theorem Thuijsman topology transition probability Vrieze X-discounted zero-sum stochastic games