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A Minority Game with Bounded Recall

Author

Listed:
  • Jérôme Renault

    (CEREMADE, Université Paris Dauphine, Pl. du Marechal de Lattre de Tassigny, F-75775 Paris Cedex 16, France)

  • Marco Scarsini

    (Dipartimento di Scienze Economiche e Aziendali, LUISS, Viale Pola 12, I-00198 Roma, Italy, and HEC, Paris)

  • Tristan Tomala

    (CEREMADE, Université Paris Dauphine, Pl. du Marechal de Lattre de Tassigny, F-75775 Paris Cedex 16, France)

Abstract

This paper studies a repeated minority game with public signals, symmetric bounded recall, and pure strategies. We investigate both public and private equilibria of the game with fixed recall size. We first show how public equilibria in such a repeated game can be represented as colored subgraphs of a de Bruijn graph. Then we prove that the set of public equilibrium payoffs with bounded recall converges to the set of uniform equilibrium payoffs as the size of the recall increases. We also show that private equilibria behave badly: A private equilibrium payoff with bounded recall need not be a uniform equilibrium payoff.

Suggested Citation

  • Jérôme Renault & Marco Scarsini & Tristan Tomala, 2007. "A Minority Game with Bounded Recall," Mathematics of Operations Research, INFORMS, vol. 32(4), pages 873-889, November.
    • Handle: RePEc:inm:ormoor:v:32:y:2007:i:4:p:873-889
    DOI: 10.1287/moor.1070.0284
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    References listed on IDEAS

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    Cited by:

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    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.
    3. Kutay Cingiz & János Flesch & P. Jean-Jacques Herings & Arkadi Predtetchinski, 2020. "Perfect information games where each player acts only once," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 69(4), pages 965-985, June.
    4. Doraszelski, Ulrich & Escobar, Juan F., 2012. "Restricted feedback in long term relationships," Journal of Economic Theory, Elsevier, vol. 147(1), pages 142-161.
    5. 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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