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Repeated games with one-memory

Barlo, Mehmet and Carmona, Guilherme and Sabourian, Hamid (2009) Repeated games with one-memory. Journal of Economic Theory, 144 (1). pp. 312-336. ISSN 0022-0531

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Official URL: http://dx.doi.org/10.1016/j.jet.2008.04.003

Abstract

We study the extent to which equilibrium payoffs of discounted repeated games can be obtained by 1-memory strategies. We establish the following in games with perfect (rich) action spaces: First, when the players are sufficiently patient, the subgame perfect Folk Theorem holds with 1-memory. Second, for arbitrary level of discounting, all strictly enforceable subgame perfect equilibrium payoffs can be approximately supported with 1-memory if the number of players exceeds two. Furthermore, in this case all subgame perfect equilibrium payoffs can be approximately supported by an ε-equilibrium with 1-memory. In two-player games, the same set of results hold if an additional restriction is assumed: Players must have common punishments. Finally, to illustrate the role of our assumptions, we present robust examples of games in which there is a subgame perfect equilibrium payoff profile that cannot be obtained with 1-memory. Thus, our results are the best that can be hoped for.

Item Type:Article
Uncontrolled Keywords:Repeated games; Memory; Bounded rationality; Folk Theorem
Subjects:H Social Sciences > HB Economic Theory
ID Code:11137
Deposited By:Mehmet Barlo
Deposited On:19 Dec 2008 10:06
Last Modified:25 May 2011 14:10

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