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The Regularity of the Value Function of Repeated Games with Switching Costs

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  • Yevgeny Tsodikovich

    (AMSE - Aix-Marseille Sciences Economiques - EHESS - École des hautes études en sciences sociales - AMU - Aix Marseille Université - ECM - École Centrale de Marseille - CNRS - Centre National de la Recherche Scientifique, Bar-Ilan University [Israël])

  • Xavier Venel

    (LUISS - Libera Università Internazionale degli Studi Sociali Guido Carli [Roma])

  • Anna Zseleva

    (Maastricht University [Maastricht])

Abstract

We study repeated zero-sum games where one of the players pays a certain cost each time he changes his action. We derive the properties of the value and optimal strategies as a function of the ratio between the switching costs and the stage payoffs. In particular, the strategies exhibit a robustness property and typically do not change with a small perturbation of this ratio. Our analysis extends partially to the case where the players are limited to simpler strategies that are history independent―namely, static strategies. In this case, we also characterize the (minimax) value and the strategies for obtaining it.

Suggested Citation

  • Yevgeny Tsodikovich & Xavier Venel & Anna Zseleva, 2022. "The Regularity of the Value Function of Repeated Games with Switching Costs," Post-Print hal-03868995, HAL.
    • Handle: RePEc:hal:journl:hal-03868995
    DOI: 10.1287/moor.2022.1325
    Note: View the original document on HAL open archive server: https://amu.hal.science/hal-03868995v2
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    Keywords

    Zero-sum games; Switching Costs; Repeated Games; Stochastic Games;
    All these keywords.

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