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Repeated Games with Present-Biased Preferences

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We study infinitely repeated games with observable actions, where players have present-biased (so-called (beta)-(delta)) preferences. We give a two-step procedure to characterize Strotz-Pollak equilibrium payoffs: compute the continuation payoff set using recursive techniques, and use this set to characterize the equilibrium payoff set U(beta,delta). While Strotz-Pollak equilibrium and subgame perfection differ here, the generated paths and payoffs do coincide. We then explore the cost of the present-time bias. Fixing the total present value of 1 util flow, lower (beta) or higher (delta) shrinks the payoff set. Surprisingly, unless the minimax outcome is a Nash equilibrium of the stage game, the equilibrium payoff set U(beta, delta) is not monotonic in (beta) or (delta). While the set U(beta, delta) is contained in that of a standard repeated game with greater discount factor, the present-time bias precludes any lower bound on U(beta, delta) that would easily generalize the (beta) = 1 folk-theorem.

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  • Hector Chade & Pavlo Prokopovych & Lones Smith, "undated". "Repeated Games with Present-Biased Preferences," Working Papers 2173938, Department of Economics, W. P. Carey School of Business, Arizona State University.
  • Handle: RePEc:asu:wpaper:2173938
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    9. Akin, Zafer, 2009. "Imperfect information processing in sequential bargaining games with present biased preferences," Journal of Economic Psychology, Elsevier, vol. 30(4), pages 642-650, August.
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    11. Sebastian Schweighofer-Kodritsch, 2015. "Time Preferences and Bargaining," STICERD - Theoretical Economics Paper Series /2015/568, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
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    13. Łukasz Balbus & Kevin Reffett & Łukasz Woźny, 2015. "Time consistent Markov policies in dynamic economies with quasi-hyperbolic consumers," International Journal of Game Theory, Springer;Game Theory Society, vol. 44(1), pages 83-112, February.
    14. Marco A. Haan & Dominic Hauck, 2023. "Games with possibly naive present-biased players," Theory and Decision, Springer, vol. 95(2), pages 173-203, August.
    15. John Duffy & Félix Muñoz-García, 2012. "Patience or Fairness? Analyzing Social Preferences in Repeated Games," Games, MDPI, vol. 3(1), pages 1-22, March.
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    18. Murat Yilmaz, 2018. "An Extended Survey of Time-Inconsistency and Its Applications," Bogazici Journal, Review of Social, Economic and Administrative Studies, Bogazici University, Department of Economics, vol. 32(1), pages 55-73.
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    22. Takeharu Sogo, 2019. "Competition among procrastinators," Theory and Decision, Springer, vol. 86(3), pages 325-337, May.
    23. Haan, Marco & Hauck, Dominic, 2014. "Games With Possibly Naive Hyperbolic Discounters," MPRA Paper 57960, University Library of Munich, Germany.
    24. Minwook Kang, 2015. "Welfare criteria for quasi-hyperbolic time preferences," Economics Bulletin, AccessEcon, vol. 35(4), pages 2506-2511.
    25. Lu, Shih En, 2016. "Self-control and bargaining," Journal of Economic Theory, Elsevier, vol. 165(C), pages 390-413.

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    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games

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