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Zero-sum games with charges

Author

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  • Flesch, János
  • Vermeulen, Dries
  • Zseleva, Anna

Abstract

We consider two-player zero-sum games with infinite action spaces and bounded payoff functions. The players' strategies are finitely additive probability measures, called charges. Since a strategy profile does not always induce a unique expected payoff, we distinguish two extreme attitudes of players. A player is viewed as pessimistic if he always evaluates the range of possible expected payoffs by the worst one, and a player is viewed as optimistic if he always evaluates it by the best one. This approach results in a definition of a pessimistic and an optimistic guarantee level for each player. We provide an extensive analysis of the relation between these guarantee levels, and connect them to the classical guarantee levels, and to other known techniques to define expected payoffs, based on computation of double integrals. In addition, we also examine existence of optimal strategies with respect to these guarantee levels.

Suggested Citation

  • Flesch, János & Vermeulen, Dries & Zseleva, Anna, 2017. "Zero-sum games with charges," Games and Economic Behavior, Elsevier, vol. 102(C), pages 666-686.
    • Handle: RePEc:eee:gamebe:v:102:y:2017:i:c:p:666-686
    DOI: 10.1016/j.geb.2016.10.014
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    References listed on IDEAS

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    Cited by:

    1. János Flesch & Dries Vermeulen & Anna Zseleva, 2019. "Catch games: the impact of modeling decisions," International Journal of Game Theory, Springer;Game Theory Society, vol. 48(2), pages 513-541, June.
    2. Flesch, Janos & Vermeulen, Dries & Zseleva, Anna, 2018. "Existence of justifiable equilibrium," Research Memorandum 016, Maastricht University, Graduate School of Business and Economics (GSBE).
    3. János Flesch & Dries Vermeulen & Anna Zseleva, 2021. "Legitimate equilibrium," International Journal of Game Theory, Springer;Game Theory Society, vol. 50(4), pages 787-800, December.

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    More about this item

    Keywords

    Infinite games; Two-person zero-sum games; Finitely additive strategies; The Wald game;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

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