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Repeated Games with Present-Biased Preferences



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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    References listed on IDEAS

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    Cited by:

    1. Yılmaz, Murat, 2013. "Repeated moral hazard with a time-inconsistent agent," Journal of Economic Behavior & Organization, Elsevier, vol. 95(C), pages 70-89.
    2. Ahmet Altiok & Murat Yilmaz, 2014. "Dynamic Voluntary Contribution to a Public Project under Time-Inconsistency," Working Papers 2014/08, Bogazici University, Department of Economics.
    3. Bernergård, Axel, 2011. "Folk Theorems for Present-Biased Players," SSE/EFI Working Paper Series in Economics and Finance 736, Stockholm School of Economics.
    4. 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.
    5. repec:eee:jeborg:v:145:y:2018:i:c:p:114-140 is not listed on IDEAS
    6. 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.
    7. 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.
    8. John Duffy & Félix Muñoz-García, 2012. "Patience or Fairness? Analyzing Social Preferences in Repeated Games," Games, MDPI, Open Access Journal, vol. 3(1), pages 1-22, March.
    9. Doraszelski, Ulrich & Escobar, Juan F., 2012. "Restricted feedback in long term relationships," Journal of Economic Theory, Elsevier, vol. 147(1), pages 142-161.
    10. Haan, Marco & Hauck, Dominic, 2014. "Games With Possibly Naive Hyperbolic Discounters," MPRA Paper 57960, University Library of Munich, Germany.
    11. repec:eee:jetheo:v:172:y:2017:i:c:p:348-375 is not listed on IDEAS
    12. Łukasz Balbus & Łukasz Woźny, 2016. "A Strategic Dynamic Programming Method for Studying Short-Memory Equilibria of Stochastic Games with Uncountable Number of States," Dynamic Games and Applications, Springer, vol. 6(2), pages 187-208, June.
    13. Minwook Kang, 2015. "Welfare criteria for quasi-hyperbolic time preferences," Economics Bulletin, AccessEcon, vol. 35(4), pages 2506-2511.
    14. Ichiro Obara & Jaeok Park, 2015. "Repeated Games with General Discounting," Working papers 2015rwp-84, Yonsei University, Yonsei Economics Research Institute.
    15. 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.
    16. Lu, Shih En, 2016. "Self-control and bargaining," Journal of Economic Theory, Elsevier, vol. 165(C), pages 390-413.

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    JEL classification:

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

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