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Switching Costs in Infinitely Repeated Games

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  • Lipman, Barton
  • Wang, Ruqu

Abstract

We show that small switching costs can have surprisingly dramatic effects in infinitely repeated games if these costs are large relative to payoffs in a single period. This shows that the results in Lipman and Wang [2000] do have analogs in the case of infinitely repeated games. We also discuss whether the results here or those in Lipman–Wang [2000] imply a discontinuity in the equilibrium outcome correspondence with respect to small switching costs. We conclude that there is not a discontinuity with respect to switching costs but that the switching costs do create a discontinuity with respect to the length of a period.
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Suggested Citation

  • Lipman, Barton & Wang, Ruqu, 2006. "Switching Costs in Infinitely Repeated Games," Queen's Economics Department Working Papers 273471, Queen's University - Department of Economics.
    • Handle: RePEc:ags:quedwp:273471
    DOI: 10.22004/ag.econ.273471
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    References listed on IDEAS

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    1. Drew Fudenberg & David Levine, 2008. "Subgame–Perfect Equilibria of Finite– and Infinite–Horizon Games," World Scientific Book Chapters, in: Drew Fudenberg & David K Levine (ed.), A Long-Run Collaboration On Long-Run Games, chapter 1, pages 3-20, World Scientific Publishing Co. Pte. Ltd..
    2. Drew Fudenberg & Jean Tirole, 1991. "Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262061414, December.
    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. Wen, Quan, 1994. "The "Folk Theorem" for Repeated Games with Complete Information," Econometrica, Econometric Society, vol. 62(4), pages 949-954, July.
    5. Fudenberg, Drew & Maskin, Eric, 1991. "On the dispensability of public randomization in discounted repeated games," Journal of Economic Theory, Elsevier, vol. 53(2), pages 428-438, April.
    6. Drew Fudenberg & Eric Maskin, 2008. "The Folk Theorem In Repeated Games With Discounting Or With Incomplete Information," World Scientific Book Chapters, in: Drew Fudenberg & David K Levine (ed.), A Long-Run Collaboration On Long-Run Games, chapter 11, pages 209-230, World Scientific Publishing Co. Pte. Ltd..
    7. Dutta Prajit K., 1995. "Collusion, Discounting and Dynamic Games," Journal of Economic Theory, Elsevier, vol. 66(1), pages 289-306, June.
    8. Abreu, Dilip & Dutta, Prajit K & Smith, Lones, 1994. "The Folk Theorem for Repeated Games: A NEU Condition," Econometrica, Econometric Society, vol. 62(4), pages 939-948, July.
    9. Dutta Prajit K., 1995. "A Folk Theorem for Stochastic Games," Journal of Economic Theory, Elsevier, vol. 66(1), pages 1-32, June.
    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. 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.
    12. Chakrabarti, Subir K., 1990. "Characterizations of the equilibrium payoffs of inertia supergames," Journal of Economic Theory, Elsevier, vol. 51(1), pages 171-183, June.
    13. Benoit, Jean-Pierre & Krishna, Vijay, 1985. "Finitely Repeated Games," Econometrica, Econometric Society, vol. 53(4), pages 905-922, July.
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    Citations

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    Cited by:

    1. Yevgeny Tsodikovich & Ehud Lehrer, 2019. "Stochastic revision opportunities in Markov decision problems," Annals of Operations Research, Springer, vol. 279(1), pages 251-270, August.
    2. 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.
    3. Lehrer, Ehud & Solan, Eilon, 2018. "High frequency repeated games with costly monitoring," Theoretical Economics, Econometric Society, vol. 13(1), January.
    4. Aramendia, Miguel & Wen, Quan, 2020. "Myopic perception in repeated games," Games and Economic Behavior, Elsevier, vol. 119(C), pages 1-14.
    5. Yevgeny Tsodikovich & Xavier Venel & Anna Zseleva, 2021. "Repeated Games with Switching Costs: Stationary vs History-Independent Strategies," Working Papers halshs-03223279, HAL.
    6. Guney, Begum & Richter, Michael, 2018. "Costly switching from a status quo," Journal of Economic Behavior & Organization, Elsevier, vol. 156(C), pages 55-70.
    7. Yevgeny Tsodikovich & Xavier Venel & Anna Zseleva, 2024. "The Price of History-Independent Strategies in Games with Inter-Temporal Externalities," Dynamic Games and Applications, Springer, vol. 14(5), pages 1317-1332, November.
    8. Dai Zusai, 2018. "Tempered best response dynamics," International Journal of Game Theory, Springer;Game Theory Society, vol. 47(1), pages 1-34, March.
    9. Yevgeny Tsodikovich & Xavier Venel & Anna Zseleva, 2022. "Folk Theorems in Repeated Games with Switching Costs," Working Papers hal-03888188, HAL.
    10. Lipman, Barton L. & Wang, Ruqu, 2009. "Switching costs in infinitely repeated games," Games and Economic Behavior, Elsevier, vol. 66(1), pages 292-314, May.
    11. Tsodikovich, Yevgeny & Venel, Xavier & Zseleva, Anna, 2024. "Folk theorems in repeated games with switching costs," Games and Economic Behavior, Elsevier, vol. 146(C), pages 137-159.
    12. 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.
    13. Francesc Dilmé & Daniel F Garrett, 2019. "Residual Deterrence," Journal of the European Economic Association, European Economic Association, vol. 17(5), pages 1654-1686.
    14. 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.
    15. Dilmé, Francesc, 2019. "Reputation building through costly adjustment," Journal of Economic Theory, Elsevier, vol. 181(C), pages 586-626.
    16. 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.
    17. 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).

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    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

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