Repeated Games with Present-Biased Preferences
Hector Chade,
Pavlo Prokopovych and
Lones Smith
No 1555, Cowles Foundation Discussion Papers from Cowles Foundation for Research in Economics, Yale University
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: beta-delta preferences; repeated games; dynamic programming; Strotz-Pollak equilibrium (search for similar items in EconPapers)
JEL-codes: C73 (search for similar items in EconPapers)
Pages: 24 pages
Date: 2006-01
New Economics Papers: this item is included in nep-gth
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Citations: View citations in EconPapers (2)
Published in Journal of Economic Theory (March 2008), 139(1): 157-175
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