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Repeated Games with General Discounting

Author

Listed:
  • Ichiro Obara

    (University of California)

  • Jaeok Park

    (Yonsei University)

Abstract
We introduce a general class of time discounting, which includes time-inconsistent ones, into repeated games with perfect monitoring. A strategy pro le is called an agent subgame perfect equilibrium if there is no pro table one-shot deviation at any history. We characterize strongly symmetric agent subgame perfect equilibria for repeated games with symmetric stage game. We nd that the harshest punishment takes different forms given different biases. When players are future biased, the harshest punishment is supported by a version of stick-and-carrot strategy. When players are present biased, the harshest punishment may take a more complex form. In particular, the worst punishment path may need to be cyclical. We also nd that the worst punishment payoff is different from the stage game minmax payoff even when players are patient. For some class of discounting, we show that the worst punishment payoff is larger than the stage game minmax payoff with present bias and smaller than the stage game minmax payo with future bias. We also characterize the set of limit equilibrium payoffs as the length of periods converges to 0, without changing the intertemporal structure of biases.

Suggested Citation

  • Ichiro Obara & Jaeok Park, 2015. "Repeated Games with General Discounting," Working papers 2015rwp-84, Yonsei University, Yonsei Economics Research Institute.
    • Handle: RePEc:yon:wpaper:2015rwp-84
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    References listed on IDEAS

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    Cited by:

    1. Balbus, Łukasz & Reffett, Kevin & Woźny, Łukasz, 2022. "Time-consistent equilibria in dynamic models with recursive payoffs and behavioral discounting," Journal of Economic Theory, Elsevier, vol. 204(C).
    2. Bernergård, Axel, 2019. "Self-control problems and the folk theorem," Journal of Economic Behavior & Organization, Elsevier, vol. 163(C), pages 332-347.
    3. Obara, Ichiro & Park, Jaeok, 2017. "Repeated games with general discounting," Journal of Economic Theory, Elsevier, vol. 172(C), pages 348-375.
    4. Kim, Jeongbin & Lim, Wooyoung & Schweighofer-Kodritsch, Sebastian, 2020. "Bargaining and Time Preferences: An Experimental Study," Rationality and Competition Discussion Paper Series 254, CRC TRR 190 Rationality and Competition.
    5. Yixuan Shi, 2022. "Dynamic Volunteer's Dilemma with Procrastinators," Working Papers tax-mpg-rps-2022-17, Max Planck Institute for Tax Law and Public Finance.
    6. Doruk Cetemen & Felix Zhiyu Feng & Can Urgun, 2019. "Contracting with Non-Exponential Discounting: Moral Hazard and Dynamic Inconsistency," Working Papers 2019-17, Princeton University. Economics Department..
    7. Aramendia, Miguel & Wen, Quan, 2020. "Myopic perception in repeated games," Games and Economic Behavior, Elsevier, vol. 119(C), pages 1-14.
    8. Jeongbin Kim & Wooyoung Lim & Sebastian Schweighofer-Kodritsch, 2023. "Patience Is Power: Bargaining and Payoff Delay," Berlin School of Economics Discussion Papers 0015, Berlin School of Economics.

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    More about this item

    Keywords

    Hyperbolic Discounting; Present Bias; Repeated Game; Time Inconsistency;
    All these keywords.

    JEL classification:

    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • D03 - Microeconomics - - General - - - Behavioral Microeconomics: Underlying Principles

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