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Two -person zero-sum stochastic games with semicontinuous payoff

Author

Listed:
  • 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)

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.

Suggested Citation

  • Rida Laraki & A.P. Maitra & William Sudderth, 2005. "Two -person zero-sum stochastic games with semicontinuous payoff," Working Papers hal-00243014, HAL.
    • Handle: RePEc:hal:wpaper:hal-00243014
    Note: View the original document on HAL open archive server: https://hal.science/hal-00243014
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    References listed on IDEAS

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    1. Mertens, J.-F. & Parthasarathy, T., 1987. "Equilibria for discounted stochastic games," LIDAM Discussion Papers CORE 1987050, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    2. Mertens, Jean-Francois, 2002. "Stochastic games," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 3, chapter 47, pages 1809-1832, Elsevier.
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