IDEAS home Printed from https://ideas.repec.org/p/hal/wpaper/halshs-03223279.html
   My bibliography  Save this paper

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

Author

Listed:
  • 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

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

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
    as

    Download full text from publisher

    File URL: https://shs.hal.science/halshs-03223279/document
    Download Restriction: no
    ---><---

    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.
    4. Caruana, Guillermo & Einav, Liran & Quint, Daniel, 2007. "Multilateral bargaining with concession costs," Journal of Economic Theory, Elsevier, vol. 132(1), pages 147-166, January.
    5. 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.
    6. Beggs, Alan W & Klemperer, Paul, 1992. "Multi-period Competition with Switching Costs," Econometrica, Econometric Society, vol. 60(3), pages 651-666, May.
    7. 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.
    8. T. E. S. Raghavan & Zamir Syed, 2002. "Computing Stationary Nash Equilibria of Undiscounted Single-Controller Stochastic Games," Mathematics of Operations Research, INFORMS, vol. 27(2), pages 384-400, May.
    9. Chakrabarti, Subir K., 1990. "Characterizations of the equilibrium payoffs of inertia supergames," Journal of Economic Theory, Elsevier, vol. 51(1), pages 171-183, June.
    10. 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.
    11. 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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Yevgeny Tsodikovich & Xavier Venel & Anna Zseleva, 2021. "Repeated Games with Switching Costs: Stationary vs History-Independent Strategies," AMSE Working Papers 2129, Aix-Marseille School of Economics, France.
    2. 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.
    3. Yevgeny Tsodikovich & Xavier Venel & Anna Zseleva, 2022. "Folk Theorems in Repeated Games with Switching Costs," Working Papers hal-03888188, HAL.
    4. Lipman, Barton L. & Wang, Ruqu, 2009. "Switching costs in infinitely repeated games," Games and Economic Behavior, Elsevier, vol. 66(1), pages 292-314, May.
    5. Guney, Begum & Richter, Michael, 2018. "Costly switching from a status quo," Journal of Economic Behavior & Organization, Elsevier, vol. 156(C), pages 55-70.
    6. Yu, Fengyuan & Wang, Jianwei & Chen, Wei & He, Jialu, 2023. "Increased cooperation potential and risk under suppressed strategy differentiation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 621(C).
    7. Dutta, Rohan & Ishii, Ryosuke, 2016. "Dynamic commitment games, efficiency and coordination," Journal of Economic Theory, Elsevier, vol. 163(C), pages 699-727.
    8. Kurokawa, Shun, 2019. "How memory cost, switching cost, and payoff non-linearity affect the evolution of persistence," Applied Mathematics and Computation, Elsevier, vol. 341(C), pages 174-192.
    9. Dai Zusai, 2018. "Tempered best response dynamics," International Journal of Game Theory, Springer;Game Theory Society, vol. 47(1), pages 1-34, March.
    10. Lipman, Barton L. & Wang, Ruqu, 2000. "Switching Costs in Frequently Repeated Games," Journal of Economic Theory, Elsevier, vol. 93(2), pages 149-190, August.
    11. Dilmé, Francesc, 2019. "Reputation building through costly adjustment," Journal of Economic Theory, Elsevier, vol. 181(C), pages 586-626.
    12. Barton L. Lipman & Ruqu Wang, 2006. "Switching Costs in Infinitely Repeated Games1," Boston University - Department of Economics - Working Papers Series WP2006-003, Boston University - Department of Economics.
    13. Yevgeny Tsodikovich & Ehud Lehrer, 2019. "Stochastic revision opportunities in Markov decision problems," Annals of Operations Research, Springer, vol. 279(1), pages 251-270, August.
    14. Martzoukos, Spiros H. & Zacharias, Eleftherios, 2013. "Real option games with R&D and learning spillovers," Omega, Elsevier, vol. 41(2), pages 236-249.
    15. Francesc Dilmé & Daniel F Garrett, 2019. "Residual Deterrence," Journal of the European Economic Association, European Economic Association, vol. 17(5), pages 1654-1686.
    16. Aramendia, Miguel & Wen, Quan, 2020. "Myopic perception in repeated games," Games and Economic Behavior, Elsevier, vol. 119(C), pages 1-14.
    17. Luca Lambertini & Raimondello Orsini, 2013. "On Hotelling's ‘stability in competition’ with network externalities and switching costs," Papers in Regional Science, Wiley Blackwell, vol. 92(4), pages 873-883, November.
    18. Andersen, Torben M., 1995. "Adjustment costs and price and quantity adjustment," Economics Letters, Elsevier, vol. 47(3-4), pages 343-349, March.
    19. Haltiwanger, John & Waldman, Michael, 1991. "Responders versus Non-responders: A New Perspective on Heterogeneity," Economic Journal, Royal Economic Society, vol. 101(408), pages 1085-1102, September.
    20. Emilio Fernandez-Corugedo, 2004. "Consumption Theory," Handbooks, Centre for Central Banking Studies, Bank of England, number 23, April.

    More about this item

    Keywords

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

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:hal:wpaper:halshs-03223279. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: CCSD (email available below). General contact details of provider: https://hal.archives-ouvertes.fr/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.