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

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  • Barlo, Mehmet
  • Carmona, Guilherme

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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Paper provided by Universidade Nova de Lisboa, Faculdade de Economia in its series FEUNL Working Paper Series with number wp449.

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Length: 11 pages
Date of creation: 2004
Date of revision:
Handle: RePEc:unl:unlfep:wp449

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  1. Neyman, Abraham, 1985. "Bounded complexity justifies cooperation in the finitely repeated prisoners' dilemma," Economics Letters, Elsevier, vol. 19(3), pages 227-229.
  2. Harold L. Cole & Narayana R. Kocherlakota, 2001. "Finite memory and imperfect monitoring," Staff Report 287, Federal Reserve Bank of Minneapolis.
  3. Ariel Rubinstein, 1997. "Finite automata play the repeated prisioners dilemma," Levine's Working Paper Archive 1639, David K. Levine.
  4. Barlo, Mehmet & Carmona, Guilherme & Sabourian, Hamid, 2009. "Repeated games with one-memory," Journal of Economic Theory, Elsevier, vol. 144(1), pages 312-336, January.
  5. Kalai, Ehud & Stanford, William, 1988. "Finite Rationality and Interpersonal Complexity in Repeated Games," Econometrica, Econometric Society, vol. 56(2), pages 397-410, March.
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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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