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Subgame maxmin strategies in zero-sum stochastic games with tolerance levels

Author

Listed:
  • Flesch, Janos

    (QE Math. Economics & Game Theory, RS: GSBE ETBC, RS: GSBE Theme Conflict & Cooperation)

  • Herings, P. Jean-Jacques

    (Microeconomics & Public Economics, RS: GSBE ETBC, RS: GSBE Theme Conflict & Cooperation, RS: GSBE Theme Data-Driven Decision-Making)

  • Maes, Jasmine

    (Microeconomics & Public Economics, RS: GSBE ETBC, RS: GSBE Theme Conflict & Cooperation)

  • Predtetchinski, Arkadi

    (Microeconomics & Public Economics, RS: GSBE ETBC, RS: GSBE Theme Conflict & Cooperation)

Abstract

We study subgame φ-maxmin strategies in two-player zero-sum stochastic games with finite action spaces and a countable state space. Here φ denotes the tolerance function, a function which assigns a non-negative tolerated error level to every subgame. Subgame φ-maxmin strategies are strategies of the maximizing player that guarantee the lower value in every subgame within the subgame-dependent tolerance level as given by φ. First, we provide necessary and sufficient conditions for a strategy to be a subgame φ-maxmin strategy. As a special case we obtain a characterization for subgame maxmin strategies, i.e. strategies that exactly guarantee the lower value at every subgame. Secondly, we present sufficient conditions for the existence of a subgame φ-maxmin strategy. Finally, we show the possibly surprising result that the existence of subgame φ-maxmin strategies for every positive tolerance function φ is equivalent to the existence of a subgame maxmin strategy.

Suggested Citation

  • Flesch, Janos & Herings, P. Jean-Jacques & Maes, Jasmine & Predtetchinski, Arkadi, 2018. "Subgame maxmin strategies in zero-sum stochastic games with tolerance levels," Research Memorandum 020, Maastricht University, Graduate School of Business and Economics (GSBE).
    • Handle: RePEc:unm:umagsb:2018020
    DOI: 10.26481/umagsb.2018020
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    References listed on IDEAS

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    6. János Flesch & P. Jean-Jacques Herings & Jasmine Maes & Arkadi Predtetchinski, 2021. "Subgame Maxmin Strategies in Zero-Sum Stochastic Games with Tolerance Levels," Dynamic Games and Applications, Springer, vol. 11(4), pages 704-737, December.
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    Cited by:

    1. János Flesch & P. Jean-Jacques Herings & Jasmine Maes & Arkadi Predtetchinski, 2021. "Subgame Maxmin Strategies in Zero-Sum Stochastic Games with Tolerance Levels," Dynamic Games and Applications, Springer, vol. 11(4), pages 704-737, December.
    2. Duvocelle, Benoit & Flesch, János & Staudigl, Mathias & Vermeulen, Dries, 2022. "A competitive search game with a moving target," European Journal of Operational Research, Elsevier, vol. 303(2), pages 945-957.

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    JEL classification:

    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games

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