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Repeated Games with Present-Biased Preferences

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Author Info
Hector Chade (Dept. of Economics, Arizona State University)
Pavlo Prokopovych (EERC)
Lones Smith (Dept. of Economics, 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 then 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 nonetheless 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 separately monotonic in beta or delta. While U(beta,delta) is contained in payoff set of a standard repeated game with smaller 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 Cowles Foundation, Yale University in its series Cowles Foundation Discussion Papers with number 1555.

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Length: 24 pages
Date of creation: Jan 2006
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Handle: RePEc:cwl:cwldpp:1555

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Related research
Keywords: beta-delta preferences; repeated games; dynamic programming; Strotz-Pollak equilibrium;

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Find related papers by JEL classification:
C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games

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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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