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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

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    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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