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Repeated Games with Switching Costs: Stationary vs History Independent Strategies

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  • Yevgeny Tsodikovich
  • Xavier Venel
  • Anna Zseleva

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.

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  • Yevgeny Tsodikovich & Xavier Venel & Anna Zseleva, 2021. "Repeated Games with Switching Costs: Stationary vs History Independent Strategies," Papers 2103.00045, arXiv.org, revised Oct 2021.
    • Handle: RePEc:arx:papers:2103.00045
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    References listed on IDEAS

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    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. Akerlof, George A & Yellen, Janet L, 1985. "Can Small Deviations from Rationality Make Significant Differences to Economic Equilibria?," American Economic Review, American Economic Association, vol. 75(4), pages 708-720, September.
    3. Lipman, Barton L. & Wang, Ruqu, 2009. "Switching costs in infinitely repeated games," Games and Economic Behavior, Elsevier, vol. 66(1), pages 292-314, May.
    4. Beggs, Alan W & Klemperer, Paul, 1992. "Multi-period Competition with Switching Costs," Econometrica, Econometric Society, vol. 60(3), pages 651-666, May.
    5. 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.
    6. Jerzy A. Filar & T. E. S. Raghavan, 1984. "A Matrix Game Solution of the Single-Controller Stochastic Game," Mathematics of Operations Research, INFORMS, vol. 9(3), pages 356-362, August.
    7. Stefan Rass & Sandra König & Stefan Schauer, 2017. "Defending Against Advanced Persistent Threats Using Game-Theory," PLOS ONE, Public Library of Science, vol. 12(1), pages 1-43, January.
    8. Jasmin Wachter & Stefan Rass & Sandra König, 2018. "Security from the Adversary’s Inertia–Controlling Convergence Speed When Playing Mixed Strategy Equilibria," Games, MDPI, vol. 9(3), pages 1-15, August.
    9. Caruana, Guillermo & Einav, Liran & Quint, Daniel, 2007. "Multilateral bargaining with concession costs," Journal of Economic Theory, Elsevier, vol. 132(1), pages 147-166, January.
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