Repeated games with one-memory

Mehmet Barlo, Guilherme Carmona, Hamid Sabourian

Research output: Contribution to journalArticlepeer-review

23 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)312-336
Number of pages25
JournalJournal of Economic Theory
Issue number1
Publication statusPublished - 1 Jan 2009


  • Bounded rationality
  • Folk Theorem
  • Memory
  • Repeated games


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