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The Folk Theorem with Endogenous Discounting and Unobserved Mixtures

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  • Asen Kochov
  • Yangwei Song

Abstract

We study infinitely repeated games in which the players’ rates of time preference may evolve endogenously in the course of the game. Our goal is to strengthen the folk theorem of Kochov and Song (2023) by relaxing the assumption of observable mixtures. To that end, we identify and impose a new sufficient condition on preferences. The condition holds automatically in the standard case of time-separable utilities and a common discount factor, while being generic in ours.

Suggested Citation

  • Asen Kochov & Yangwei Song, 2025. "The Folk Theorem with Endogenous Discounting and Unobserved Mixtures," CESifo Working Paper Series 12066, CESifo.
    • Handle: RePEc:ces:ceswps:_12066
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    References listed on IDEAS

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    1. 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.
    2. Chew, Soo Hong, 1983. "A Generalization of the Quasilinear Mean with Applications to the Measurement of Income Inequality and Decision Theory Resolving the Allais Paradox," Econometrica, Econometric Society, vol. 51(4), pages 1065-1092, July.
    3. 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..
    4. 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.
    5. Obara, Ichiro & Park, Jaeok, 2017. "Repeated games with general discounting," Journal of Economic Theory, Elsevier, vol. 172(C), pages 348-375.
    6. Asen Kochov & Yangwei Song, 2023. "Intertemporal Hedging and Trade in Repeated Games With Recursive Utility," Econometrica, Econometric Society, vol. 91(6), pages 2333-2369, November.
    7. Tadashi Sekiguchi & Katsutoshi Wakai, 2016. "Repeated Games with Recursive Utility:Cournot Duopoly under Gain/Loss Asymmetry," Discussion papers e-16-006, Graduate School of Economics , Kyoto University.
    8. Ehud Lehrer & Ady Pauzner, 1999. "Repeated Games with Differential Time Preferences," Econometrica, Econometric Society, vol. 67(2), pages 393-412, March.
    9. Epstein, Larry G., 1983. "Stationary cardinal utility and optimal growth under uncertainty," Journal of Economic Theory, Elsevier, vol. 31(1), pages 133-152, October.
    10. David Laibson, 1997. "Golden Eggs and Hyperbolic Discounting," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 112(2), pages 443-478.
    11. ,, 2015. "Characterizing the limit set of PPE payoffs with unequal discounting," Theoretical Economics, Econometric Society, vol. 10(3), September.
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