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Determinacy of games with Stochastic Eventual Perfect Monitoring

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  • Arieli, Itai
  • Levy, Yehuda John

Abstract

We consider an infinite two-player stochastic zero-sum game with a Borel winning set, in which the opponent's actions are monitored via stochastic private signals. We introduce two conditions of the signalling structure: Stochastic Eventual Perfect Monitoring (SEPM) and Weak Stochastic Eventual Perfect Monitoring (WSEPM). When signals are deterministic these two conditions coincide and by a recent result due to Shmaya (2011) entail determinacy of the game. We generalize Shmaya's (2011) result and show that in the stochastic learning environment SEPM implies determinacy while WSEPM does not.

Suggested Citation

  • Arieli, Itai & Levy, Yehuda John, 2015. "Determinacy of games with Stochastic Eventual Perfect Monitoring," Games and Economic Behavior, Elsevier, vol. 91(C), pages 166-185.
    • Handle: RePEc:eee:gamebe:v:91:y:2015:i:c:p:166-185
    DOI: 10.1016/j.geb.2015.04.003
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    More about this item

    Keywords

    Zero-sum stochastic games; Determinacy; Stochastic Eventual Perfect Monitoring;
    All these keywords.

    JEL classification:

    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness

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