Repeated Games with Present-Biased Preferences

25 Pages Posted: 20 Feb 2006

See all articles by Hector Chade

Hector Chade

Arizona State University (ASU) - Economics Department

Pavlo Prokopovych

Kyiv School of Economics

Lones Smith

University of Wisconsin at Madison - Department of Economics

Multiple version iconThere are 2 versions of this paper

Date Written: January 2006

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.

Keywords: Hyperbolic discounting, quasi-geometric discounting, repeated games, admissibility, continuation values

JEL Classification: C73

Suggested Citation

Chade, Hector and Prokopovych, Pavlo and Smith, Lones, Repeated Games with Present-Biased Preferences (January 2006). Cowles Foundation Discussion Paper No. 1555, Available at SSRN: https://ssrn.com/abstract=629521

Hector Chade

Arizona State University (ASU) - Economics Department ( email )

PO Box 873806
Tempe, AZ 85287-3806
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480-965-3531 (Phone)
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Pavlo Prokopovych

Kyiv School of Economics ( email )

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Kyiv, 04119
Ukraine

Lones Smith (Contact Author)

University of Wisconsin at Madison - Department of Economics ( email )

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Madison, WI 53706-1393
United States
608-263-3871 (Phone)
608-262-2033 (Fax)

HOME PAGE: http://www.lonessmith.com

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