Repeated games with one-memory

Mehmet Barlo, Guilherme Carmona () and Hamid Sabourian

Journal of Economic Theory, 2009, vol. 144, issue 1, pages 312-336

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 [epsilon]-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.

Keywords: Repeated; games; Memory; Bounded; rationality; Folk; Theorem (search for similar items in EconPapers)
Date: 2009
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Persistent link: http://EconPapers.repec.org/RePEc:eee:jetheo:v:144:y:2009:i:1:p:312-336

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