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

Author

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  • Yevgeny Tsodikovich

    (Aix-Marseille School of Economics, French National Centre for Scientific Research (CNRS), Aix Marseille University, 13205 Marseille, France; Department of Economics, Faculty of Social Sciences, Bar-Ilan University, 5290002 Ramat-Gan, Israel)

  • Xavier Venel

    (Dipartimento di Economia e Finanza, Luiss University, 00197 Rome, Italy)

  • Anna Zseleva

    (Department of Quantitative Economics, School of Business and Economics, Maastricht University, 6200 MD Maastricht, Netherlands)

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, 2023. "The Regularity of the Value Function of Repeated Games with Switching Costs," Mathematics of Operations Research, INFORMS, vol. 48(4), pages 1899-1905, November.
    • Handle: RePEc:inm:ormoor:v:48:y:2023:i:4:p:1899-1905
    DOI: 10.1287/moor.2022.1325
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