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Equilibrium Behaviors in Repeated Games

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  • Yingkai Li
  • Harry Pei

Abstract

We examine a patient player's behavior when he can build reputations in front of a sequence of myopic opponents. With positive probability, the patient player is a commitment type who plays his Stackelberg action in every period. We characterize the patient player's action frequencies in equilibrium. Our results clarify the extent to which reputations can refine the patient player's behavior and provide new insights to entry deterrence, business transactions, and capital taxation. Our proof makes a methodological contribution by establishing a new concentration inequality.

Suggested Citation

  • Yingkai Li & Harry Pei, 2020. "Equilibrium Behaviors in Repeated Games," Papers 2007.14002, arXiv.org, revised Feb 2021.
    • Handle: RePEc:arx:papers:2007.14002
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    References listed on IDEAS

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    1. Liu, Qingmin & Skrzypacz, Andrzej, 2014. "Limited records and reputation bubbles," Journal of Economic Theory, Elsevier, vol. 151(C), pages 2-29.
    2. Barro, Robert J., 1986. "Reputation in a model of monetary policy with incomplete information," Journal of Monetary Economics, Elsevier, vol. 17(1), pages 3-20, January.
    3. Phelan, Christopher, 2006. "Public trust and government betrayal," Journal of Economic Theory, Elsevier, vol. 130(1), pages 27-43, September.
    4. Ekmekci, Mehmet, 2011. "Sustainable reputations with rating systems," Journal of Economic Theory, Elsevier, vol. 146(2), pages 479-503, March.
    5. George J. Mailath & Larry Samuelson, 2001. "Who Wants a Good Reputation?," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 68(2), pages 415-441.
    6. Shuo Liu & Harry Pei, 2017. "Monotone equilibria in signalling games," ECON - Working Papers 252, Department of Economics - University of Zurich.
    7. Heski Bar-Isaac, 2003. "Reputation and Survival: Learning in a Dynamic Signalling Model," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 70(2), pages 231-251.
    8. Drew Fudenberg & David M. Kreps & Eric S. Maskin, 1990. "Repeated Games with Long-run and Short-run Players," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 57(4), pages 555-573.
    9. Schmidt Klaus M., 1993. "Commitment through Incomplete Information in a Simple Repeated Bargaining Game," Journal of Economic Theory, Elsevier, vol. 60(1), pages 114-139, June.
    10. Kreps, David M. & Wilson, Robert, 1982. "Reputation and imperfect information," Journal of Economic Theory, Elsevier, vol. 27(2), pages 253-279, August.
    11. Liu, Shuo & Pei, Harry, 2020. "Monotone equilibria in signaling games," European Economic Review, Elsevier, vol. 124(C).
    12. Milgrom, Paul & Roberts, John, 1982. "Predation, reputation, and entry deterrence," Journal of Economic Theory, Elsevier, vol. 27(2), pages 280-312, August.
    13. Qingmin Liu, 2011. "Information Acquisition and Reputation Dynamics," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 78(4), pages 1400-1425.
    14. Mailath, George J. & Samuelson, Larry, 2006. "Repeated Games and Reputations: Long-Run Relationships," OUP Catalogue, Oxford University Press, number 9780195300796.
    15. Harry Pei, 2020. "Reputation Effects Under Interdependent Values," Econometrica, Econometric Society, vol. 88(5), pages 2175-2202, September.
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    Cited by:

    1. Fazal-e-Hasan, Syed Muhammad & Ahmadi, Hormoz & Mortimer, Gary & Sekhon, Harjit & Kharouf, Husni & Jebarajakirthy, Charles, 2020. "The interplay of positive and negative emotions to quit unhealthy consumption behaviors: Insights for social marketers," Australasian marketing journal, Elsevier, vol. 28(4), pages 349-360.
    2. Harry Pei, 2022. "Reputation Effects under Short Memories," Papers 2207.02744, arXiv.org, revised Jan 2023.

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