Two -person zero-sum stochastic games with semicontinuous payoff

Rida Laraki (), A.P. Maitra and William Sudderth
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Rida Laraki: CECO - Laboratoire d'économétrie de l'École polytechnique - X - École polytechnique - IP Paris - Institut Polytechnique de Paris - CNRS - Centre National de la Recherche Scientifique
A.P. Maitra: CECO - Laboratoire d'économétrie de l'École polytechnique - X - École polytechnique - IP Paris - Institut Polytechnique de Paris - CNRS - Centre National de la Recherche Scientifique
William Sudderth: CECO - Laboratoire d'économétrie de l'École polytechnique - X - École polytechnique - IP Paris - Institut Polytechnique de Paris - CNRS - Centre National de la Recherche Scientifique

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Abstract: Consider a two-person zero-sum stochastic game with Borel state space S, compact metric action sets A, B and law of motion q such that the integral under q of every bounded Borel measurable function depends measurably on the initial state s and continuously on the actions (a,b) of the players. Suppose the payoff is a bounded function f of the infinite history of states and actions such that f is measurable for the product of the Borel sigma-fields of the coordinate spaces and is lower semicontinuous for the product of the discrete topologies on the coordinate spaces. Then the game has a value and player II has a subgame perfect optimal strategy.

Date: 2005
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