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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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Paper provided by Department of Economics, W. P. Carey School of Business, Arizona State University in its series Working Papers with number 2173938.

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Handle: RePEc:asu:wpaper:2173938

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  1. Ted O'Donoghue & Matthew Rabin, 1996. "Doing It Now or Later," Discussion Papers 1172, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
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Cited by:
  1. John Duffy & Felix Munoz-Garcia, 2009. "Patience or Fairness? Analyzing Social Preferences in Repeated Games," Working Papers 383, University of Pittsburgh, Department of Economics, revised May 2009.
  2. Bernergård, Axel, 2011. "Folk Theorems for Present-Biased Players," Working Paper Series in Economics and Finance 736, Stockholm School of Economics.
  3. Yılmaz, Murat, 2013. "Repeated moral hazard with a time-inconsistent agent," Journal of Economic Behavior & Organization, Elsevier, vol. 95(C), pages 70-89.
  4. Doraszelski, Ulrich & Escobar, Juan F., 2012. "Restricted feedback in long term relationships," Journal of Economic Theory, Elsevier, vol. 147(1), pages 142-161.
  5. Zafer Akin, 2008. "Imperfect Information Processing in Sequential Bargaining Games with Present Biased Preferences," Working Papers 0810, TOBB University of Economics and Technology, Department of Economics.

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