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Time dependent bounded recall strategies are enough to play the discounted repeated prisoners' dilemma

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  • Mehmet Barlo
  • Guilherme Carmona

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.

Suggested Citation

  • Mehmet Barlo & Guilherme Carmona, 2004. "Time dependent bounded recall strategies are enough to play the discounted repeated prisoners' dilemma," Nova SBE Working Paper Series wp449, Universidade Nova de Lisboa, Nova School of Business and Economics.
    • Handle: RePEc:unl:unlfep:wp449
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    References listed on IDEAS

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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. Kalai, Ehud & Stanford, William, 1988. "Finite Rationality and Interpersonal Complexity in Repeated Games," Econometrica, Econometric Society, vol. 56(2), pages 397-410, March.
    3. Cole, Harold L. & Kocherlakota, Narayana R., 2005. "Finite memory and imperfect monitoring," Games and Economic Behavior, Elsevier, vol. 53(1), pages 59-72, October.
    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. Rubinstein, Ariel, 1986. "Finite automata play the repeated prisoner's dilemma," Journal of Economic Theory, Elsevier, vol. 39(1), pages 83-96, June.
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    Cited by:

    1. 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.
    2. Mailath, George J. & Olszewski, Wojciech, 2011. "Folk theorems with bounded recall under (almost) perfect monitoring," Games and Economic Behavior, Elsevier, vol. 71(1), pages 174-192, January.

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    More about this item

    JEL classification:

    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
    • D8 - Microeconomics - - Information, Knowledge, and Uncertainty

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