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Repeated Games with Switching Costs: Stationary vs History-Independent Strategies

Author

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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)

  • Xavier Venel

    (Dipartimento di Economia e Finanza [Roma] - LUISS - Libera Università Internazionale degli Studi Sociali Guido Carli [Roma])

  • Anna Zseleva

    (Maastricht University [Maastricht])

Abstract

We study zero-sum repeated games where the minimizing player has to pay a certain cost each time he changes his action. Our contribution is twofold. First, we show that the value of the game exists in stationary strategies, depending solely on the previous action of the minimizing player, not the entire history. We provide a full characterization of the value and the optimal strategies. The strategies exhibit a robustness property and typically do not change with a small perturbation of the switching costs. Second, we consider a case where the minimizing player is limited to playing simpler strategies that are completely history-independent. Here too, we provide a full characterization of the (minimax) value and the strategies for obtaining it. Moreover, we present several bounds on the loss due to this limitation.

Suggested Citation

  • Yevgeny Tsodikovich & Xavier Venel & Anna Zseleva, 2021. "Repeated Games with Switching Costs: Stationary vs History-Independent Strategies," Working Papers halshs-03223279, HAL.
    • Handle: RePEc:hal:wpaper:halshs-03223279
    Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-03223279
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    References listed on IDEAS

    as
    1. Lipman, Barton L. & Wang, Ruqu, 2000. "Switching Costs in Frequently Repeated Games," Journal of Economic Theory, Elsevier, vol. 93(2), pages 149-190, August.
    2. Lipman, Barton L. & Wang, Ruqu, 2009. "Switching costs in infinitely repeated games," Games and Economic Behavior, Elsevier, vol. 66(1), pages 292-314, May.
    3. G. Schoenmakers & J. Flesch & F. Thuijsman & O. J. Vrieze, 2008. "Repeated Games with Bonuses," Journal of Optimization Theory and Applications, Springer, vol. 136(3), pages 459-473, March.
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    More about this item

    Keywords

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

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