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A folk theorem for repeated games with unequal discounting

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  • Chen, Bo
  • Takahashi, Satoru

Abstract

We introduce a “dynamic non-equivalent utilities” (DNEU) condition and the notion of dynamic player-specific punishments for a general repeated game with unequal discounting, both naturally generalizing the stationary counterparts in Abreu et al. (1994). We show that if the DNEU condition, i.e., no pair of players have equivalent utility functions in the repeated game, is satisfied, then any feasible and strictly sequentially individually rational payoff sequence allows dynamic player-specific punishments. Using this result, we prove a folk theorem for unequal discounting repeated games that satisfy the DNEU condition.

Suggested Citation

  • Chen, Bo & Takahashi, Satoru, 2012. "A folk theorem for repeated games with unequal discounting," Games and Economic Behavior, Elsevier, vol. 76(2), pages 571-581.
    • Handle: RePEc:eee:gamebe:v:76:y:2012:i:2:p:571-581
    DOI: 10.1016/j.geb.2012.07.011
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    Cited by:

    1. Carmona, Guilherme & Carvalho, Luís, 2016. "Repeated two-person zero-sum games with unequal discounting and private monitoring," Journal of Mathematical Economics, Elsevier, vol. 63(C), pages 131-138.
    2. Chihiro Morooka, 2021. "Equilibrium payoffs in two-player discounted OLG games," International Journal of Game Theory, Springer;Game Theory Society, vol. 50(4), pages 1021-1032, December.
    3. Kimmo Berg, 2017. "Extremal Pure Strategies and Monotonicity in Repeated Games," Computational Economics, Springer;Society for Computational Economics, vol. 49(3), pages 387-404, March.
    4. Ani Dasgupta & Sambuddha Ghosh, 2017. "Repeated Games Without Public Randomization: A Constructive Approach," Boston University - Department of Economics - Working Papers Series WP2017-011, Boston University - Department of Economics, revised Feb 2019.
    5. ,, 2015. "Characterizing the limit set of PPE payoffs with unequal discounting," Theoretical Economics, Econometric Society, vol. 10(3), September.
    6. Marina Agranov & Jeongbin Kim & Leeat Yariv, 2023. "Coordination with Differential Time Preferences: Experimental Evidence," CESifo Working Paper Series 10454, CESifo.
    7. Aramendia, Miguel & Wen, Quan, 2020. "Myopic perception in repeated games," Games and Economic Behavior, Elsevier, vol. 119(C), pages 1-14.
    8. Mitri Kitti, 2018. "Subgame Perfect Equilibria in Continuous-Time Repeated Games," Discussion Papers 120, Aboa Centre for Economics.
    9. Mitri Kitti, 2014. "Equilibrium Payoffs for Pure Strategies in Repeated Games," Discussion Papers 98, Aboa Centre for Economics.
    10. Dasgupta, Ani & Ghosh, Sambuddha, 2022. "Self-accessibility and repeated games with asymmetric discounting," Journal of Economic Theory, Elsevier, vol. 200(C).

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    More about this item

    Keywords

    Intertemporal trade; Folk theorem; Repeated game; Unequal discounting;
    All these keywords.

    JEL classification:

    • C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games

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