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Time Dependent Bounded Recall Strategies Are Enough to Play the Discounted Repeated Prisoners' Dilemma

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  • Mehmet Barlo

    (Sabanc{\i} University)

  • Guilherme Carmona

    (Universidade Nova de Lisboa)

Abstract

We show that for any discount factor, there is a natural number $M$ such that all subgame perfect equilibrium outcomes of the discounted repeated prisoners' dilemma can be obtained by subgame perfect equilibrium strategies with the following property: current play depends only on the number of the time-index and on the history of the last $M$ periods. Therefore, players who are restricted to using pure strategies, have to remember, at the most, $M$ periods in order to play any equilibrium outcome of the discounted repeated prisoners' dilemma. This result leads us to introduce the notion of time dependent complexity, and to conclude that in the repeated prisoners' dilemma, restricting attention to finite time dependent complex strategies is enough.

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File URL: http://128.118.178.162/eps/game/papers/0405/0405006.pdf
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Bibliographic Info

Paper provided by EconWPA in its series Game Theory and Information with number 0405006.

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Length: 11 pages
Date of creation: 07 May 2004
Date of revision:
Handle: RePEc:wpa:wuwpga:0405006

Note: Type of Document - pdf; pages: 11. None
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Web page: http://128.118.178.162

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Keywords: Repeated Prisoners' Dilemma; Memory; Bounded Rationality;

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  1. Rubinstein, Ariel, 1986. "Finite automata play the repeated prisoner's dilemma," Journal of Economic Theory, Elsevier, vol. 39(1), pages 83-96, June.
  2. Harold L. Cole & Narayana R. Kocherlakota, 2000. "Finite memory and imperfect monitoring," Working Papers 604, Federal Reserve Bank of Minneapolis.
  3. Kalai, Ehud & Stanford, William, 1988. "Finite Rationality and Interpersonal Complexity in Repeated Games," Econometrica, Econometric Society, vol. 56(2), pages 397-410, March.
  4. Neyman, Abraham, 1985. "Bounded complexity justifies cooperation in the finitely repeated prisoners' dilemma," Economics Letters, Elsevier, vol. 19(3), pages 227-229.
  5. Barlo, Mehmet & Carmona, Guilherme & Sabourian, Hamid, 2009. "Repeated games with one-memory," Journal of Economic Theory, Elsevier, vol. 144(1), pages 312-336, January.
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Cited by:
  1. George Mailath & Wojciech Olszewski, 2008. "Folk theorems with Bounded Recall under(Almost) Perfect Monitoring," Discussion Papers 1462, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  2. Barlo, Mehmet & Carmona, Guilherme, 2007. "One - Memory in Repeated Games," FEUNL Working Paper Series wp500, Universidade Nova de Lisboa, Faculdade de Economia.

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