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One - Memory in Repeated Games

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Author Info
Barlo, Mehmet
Carmona, Guilherme

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Abstract

We study the extent to which equilibrium payo®s 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 payo® pro¯le 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 " { sub- game perfect equilibrium strategy of 1 { memory, 2. all strictly enforceable subgame perfect equilibrium payo®s can be approximately sup- ported 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 ¯rst two: players must have common punishments.

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Paper provided by Universidade Nova de Lisboa, Faculdade de Economia in its series FEUNL Working Paper Series with number wp500.

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Length: 49 pages
Date of creation: 2007
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Handle: RePEc:unl:unlfep:wp500

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  1. Bhaskar, V. & Vega-Redondo, Fernando, 2002. "Asynchronous Choice and Markov Equilibria," Journal of Economic Theory, Elsevier, vol. 103(2), pages 334-350, April. [Downloadable!] (restricted)
  2. Aumann, Robert J. & Sorin, Sylvain, 1989. "Cooperation and bounded recall," Games and Economic Behavior, Elsevier, vol. 1(1), pages 5-39, March. [Downloadable!] (restricted)
  3. Abreu, Dilip, 1988. "On the Theory of Infinitely Repeated Games with Discounting," Econometrica, Econometric Society, vol. 56(2), pages 383-96, March. [Downloadable!] (restricted)
  4. Abreu, Dilip & Dutta, Prajit K & Smith, Lones, 1994. "The Folk Theorem for Repeated Games: A NEU Condition," Econometrica, Econometric Society, vol. 62(4), pages 939-48, July. [Downloadable!] (restricted)
  5. Lehrer, Ehud, 1988. "Repeated games with stationary bounded recall strategies," Journal of Economic Theory, Elsevier, vol. 46(1), pages 130-144, October. [Downloadable!] (restricted)
  6. Mailath, George J. & Postlewaite, Andrew & Samuelson, Larry, 2005. "Contemporaneous perfect epsilon-equilibria," Games and Economic Behavior, Elsevier, vol. 53(1), pages 126-140, October. [Downloadable!] (restricted)
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  7. Fudenberg, Drew & Maskin, Eric, 1986. "The Folk Theorem in Repeated Games with Discounting or with Incomplete Information," Econometrica, Econometric Society, vol. 54(3), pages 533-54, May. [Downloadable!] (restricted)
  8. Mehmet Barlo & Guilherme Carmona, 2004. "Time Dependent Bounded Recall Strategies Are Enough to Play the Discounted Repeated Prisoners' Dilemma," Game Theory and Information 0405006, EconWPA. [Downloadable!]
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  9. Kalai, Ehud & Stanford, William, 1988. "Finite Rationality and Interpersonal Complexity in Repeated Games," Econometrica, Econometric Society, vol. 56(2), pages 397-410, March. [Downloadable!] (restricted)
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  10. Neyman, Abraham & Okada, Daijiro, 1999. "Strategic Entropy and Complexity in Repeated Games," Games and Economic Behavior, Elsevier, vol. 29(1-2), pages 191-223, October. [Downloadable!] (restricted)
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