Stochastic Games and Applications

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Springer Science & Business Media, Oct 31, 2003 - Business & Economics - 473 pages
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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.
 

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Contents

STOCHASTIC GAMES
1
FROM MARKOV CHAINS TO STOCHASTIC GAMES
9
CLASSIFICATION AND BASIC TOOLS
27
STOCHASTIC GAMES AND STATIONARY STRATEGIES
37
THE FINITE CASE
51
REAL ALGEBRAIC TOOLS IN STOCHASTIC GAMES
57
ZEROSUM STOCHASTIC GAMES WITH BOREL STATE SPACES
77
EXTENSIONS OF THE FINITE STATE SPACE CASE AND CORRELATION
93
PERTURBATIONS OF MARKOV CHAINS WITH APPLICATIONS TO STOCHASTIC GAMES
265
A REDUCTION
281
ON A CLASS OF RECURSIVE GAMES
293
MORE THAN TWO PLAYERS
309
SYMMETRIC INCOMPLETE INFORMATION GAMES AS STOCHASTIC GAMES
323
ABSORBING GAMES WITH A SIGNALLING STRUCTURE
335
STOCHASTIC GAMES WITH LIM SUP PAYOFF
357
STOCHASTIC GAMES WITH BOREL PAYOFFS
367

A MEASURABLE MEASURABLE CHOICE THEOREM
107
EQUILIBRIA FOR DISCOUNTED STOCHASTIC GAMES
131
EXISTENCE OF THE MINMAX
173
THE BIG MATCH AND THE PARIS MATCH
195
REPEATED GAMES WITH ABSORBING STATES
205
STOCHASTIC GAMES PRACTICAL MOTIVATION AND THE ORDERFIELD PROPERTY FOR SPECIAL CLASSES
215
FINITESTEP ALGORITHMS FOR SINGLECONTROLLER AND PERFECT INFORMATION STOCHASTIC GAMES
227
RECURSIVE GAMES
253
STOCHASTIC GAMES WITH INCOMPLETE INFORMATION
375
STOCHASTIC GAMES AND NONEXPANSIVE MAPS
397
THE OPERATOR APPROACH TO ZEROSUM STOCHASTIC GAMES
417
GAMES WITH A RECURSIVE STRUCTURE
427
THE LATTICETHEORETIC APPROACH
443
AN OVERVIEW
455
Contributors
471
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