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One - memory in repeated games

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  • Mehmet Barlo
  • Guilherme Carmona

Abstract

We study the extent to which equilibrium payoffs of discounted repeated games can be obtained by 1 - memory strategies. First, we present robust examples of games in which there is a subgame perfect equilibrium payoff profile that cannot be obtained by any 1 - memory subgame perfect equilibrium. Then, a complete characterization of 1 - memory simple strategies is provided, and it is employed to establish the following in games with more than two players each having connected action spaces: 1. all subgame perfect equilibrium payo®s can be approximately supported by an " - subgame perfect equilibrium strategy of 1 - memory, 2. all strictly enforceable subgame perfect equilibrium payoffs can be approximately supported by a 1 - memory subgame equilibrium, and 3. the subgame perfect Folk Theorem holds for 1 - memory strategies. While no further restrictions are needed for the third result to hold in 2 - player games, an additional restriction is needed for the first two: players must have common punishments.

Suggested Citation

  • Mehmet Barlo & Guilherme Carmona, 2007. "One - memory in repeated games," Nova SBE Working Paper Series wp500, Universidade Nova de Lisboa, Nova School of Business and Economics.
    • Handle: RePEc:unl:unlfep:wp500
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