確率ゲームとその応用（会議録）<br>Stochastic Games and Applications (NATO Science Series II Mathematics, Physics and Chemistry)

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確率ゲームとその応用（会議録）
Stochastic Games and Applications (NATO Science Series II Mathematics, Physics and Chemistry)

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  • 製本 Hardcover:ハードカバー版／ページ数 472 p.
  • 言語 ENG
  • 商品コード 9781402014925
  • DDC分類 519.3

Full Description

This 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.

Contents

1. Stochastic games.- 2. From Markov chains to stochastic games.- 3. Classification and basic tools.- 4. Stochastic games and stationary strategies.- 5. Discounted stochastic games: The finite case.- 6. Real algebraic tools in stochastic games.- 7. Zero-sum stochastic games with borel state spaces.- 8. N-person stochastic games: extensions of the finite state space case and correlation.- 9. A measurable "measurable choice" theorem.- 10. Equilibria for discounted stochastic games.- 11. Stochastic games: existence of the minmax.- 12. The big match and the paris match.- 13. Repeated games with absorbing states.- 14. Stochastic games, practical motivation and the orderfield property for special classes.- 15. Finite-step algorithms for single-controller and perfect information stochastic games.- 16. Recursive games.- 17. Perturbations of Markov chains with applications to stochastic games.- 18. Two-player non-zero-sum games: A reduction.- 19. On a class of recursive games.- 20. Uniform equilibrium: more than two players.- 21. Symmetric incomplete information games as stochastic games.- 22. Absorbing games with a signalling structure.- 23. Stochastic Games with lim sup Payoff.- 24. Stochastic games with borel payoffs.- 25. Stochastic games with incomplete information.- 26. Stochastic games and nonexpansive maps.- 27. The operator approach to zero-sum stochastic games.- 28. Games with a recursive structure.- 29. Stochastic games in economics: The lattice-theoretic approach.- 30. Stochastic games in economics and related fields: an overview.- Contributors.