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Repeated Games with Present-Biased Preferences

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Author Info
Hector Chade () (W. P. Carey School of Business Department of Economics)
Pavlo Prokopovych (University of Michigan)
Lones Smith (University of Michigan)

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Abstract

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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  3. Jonathan Gruber & Botond Koszegi, 2000. "Is Addiction "Rational"? Theory and Evidence," NBER Working Papers 7507, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
  4. Jonathan Gruber & Botond Köszegi, 2001. "Is Addiction "Rational"? Theory And Evidence," The Quarterly Journal of Economics, MIT Press, vol. 116(4), pages 1261-1303, November. [Downloadable!] (restricted)
  5. Laibson, David, 1997. "Golden Eggs and Hyperbolic Discounting," The Quarterly Journal of Economics, MIT Press, vol. 112(2), pages 443-77, May.
  6. Kocherlakota, Narayana R., 1996. "Reconsideration-Proofness: A Refinement for Infinite Horizon Time Inconsistency," Games and Economic Behavior, Elsevier, vol. 15(1), pages 33-54, July. [Downloadable!] (restricted)
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  8. Ted O'Donoghue & Matthew Rabin, 1999. "Doing It Now or Later," American Economic Review, American Economic Association, vol. 89(1), pages 103-124, March. [Downloadable!] (restricted)
  9. Peleg, Bezalel & Yaari, Menahem E, 1973. "On the Existence of a Consistent Course of Action when Tastes are Changing," Review of Economic Studies, Blackwell Publishing, vol. 40(3), pages 391-401, July. [Downloadable!] (restricted)
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  1. 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. [Downloadable!]
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