Stochastic Games and Applications / Edition 1

by Abraham Neyman, S. Sorin

Overview

This volume is based on lectures given at the NATO Advanced Study Institute on "Shastic 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 "Shastic 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 technique, 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 shastic game the play proceeds by steps from position to position, according to transition probabilities controlled jointly by the two players.

Product Details

ISBN-13:	9781402014932
Publisher:	Springer Netherlands
Publication date:	10/31/2003
Series:	Nato Science Series C: , #570
Edition description:	Softcover reprint of the original 1st ed. 2003
Pages:	473
Product dimensions:	6.30(w) x 9.45(h) x 0.04(d)

Table of Contents

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