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The strategic value of recall

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  • Peretz, Ron

Abstract

This work studies the value of two-person zero-sum repeated games in which at least one of the players is restricted to (mixtures of) bounded recall strategies. A (pure) k-recall strategy is a strategy that relies only on the last k periods of history. This work improves previous results (Lehrer, 1988; Neyman and Okada, 2009) on repeated games with bounded recall. We provide an explicit formula for the asymptotic value of the repeated game as a function of the one-stage game, the duration of the repeated game, and the recall of the agents.

Suggested Citation

  • Peretz, Ron, 2012. "The strategic value of recall," Games and Economic Behavior, Elsevier, vol. 74(1), pages 332-351.
    • Handle: RePEc:eee:gamebe:v:74:y:2012:i:1:p:332-351
    DOI: 10.1016/j.geb.2011.05.013
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    References listed on IDEAS

    as
    1. Abraham Neyman, 2008. "Learning Effectiveness and Memory Size," Discussion Paper Series dp476, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
    2. Neyman, Abraham & Okada, Daijiro, 2009. "Growth of strategy sets, entropy, and nonstationary bounded recall," Games and Economic Behavior, Elsevier, vol. 66(1), pages 404-425, May.
    3. repec:dau:papers:123456789/6127 is not listed on IDEAS
    4. Neyman, Abraham & Okada, Daijiro, 2000. "Repeated Games with Bounded Entropy," Games and Economic Behavior, Elsevier, vol. 30(2), pages 228-247, February.
    5. Lehrer, Ehud, 1988. "Repeated games with stationary bounded recall strategies," Journal of Economic Theory, Elsevier, vol. 46(1), pages 130-144, October.
    6. Gilad Bavly & Abraham Neyman, 2003. "Online Concealed Correlation by Boundedly Rational Players," Discussion Paper Series dp336, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
    7. Renault, Jérôme & Scarsini, Marco & Tomala, Tristan, 2008. "Playing off-line games with bounded rationality," Mathematical Social Sciences, Elsevier, vol. 56(2), pages 207-223, September.
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    Citations

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    Cited by:

    1. Bavly, Gilad & Peretz, Ron, 2019. "Limits of correlation in repeated games with bounded memory," Games and Economic Behavior, Elsevier, vol. 115(C), pages 131-145.
    2. Ron Peretz, 2013. "Correlation through bounded recall strategies," International Journal of Game Theory, Springer;Game Theory Society, vol. 42(4), pages 867-890, November.
    3. Olivier Gossner & Penélope Hernández & Ron Peretz, 2016. "The complexity of interacting automata," International Journal of Game Theory, Springer;Game Theory Society, vol. 45(1), pages 461-496, March.

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    More about this item

    Keywords

    Bounded recall; Bounded memory; Bounded rationality; Repeated games; Entropy; de Bruijn sequences;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games

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