A Minority Game with Bounded Recall

Mathematics of Operations Research, Vol. 32, pp. 873-889, 2007

Posted: 12 Mar 2012

See all articles by Jerome Renault

Jerome Renault

University of Toulouse 1 - Toulouse School of Economics (TSE)

Marco Scarsini

Luiss University Dipartimento di Economia e Finanza

Tristan Tomala

HEC Paris - Economics & Decision Sciences

Date Written: 2007

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.

Keywords: folk theorem, de Bruijn sequence, imperfect monitoring, uniform equilibrium, public equilibrium, private equilibrium

JEL Classification: C72, C73

Suggested Citation

Renault, Jerome and Scarsini, Marco and Tomala, Tristan, A Minority Game with Bounded Recall (2007). Mathematics of Operations Research, Vol. 32, pp. 873-889, 2007, Available at SSRN: https://ssrn.com/abstract=2019691

Jerome Renault

University of Toulouse 1 - Toulouse School of Economics (TSE) ( email )

Place Anatole-France
Toulouse Cedex, F-31042
France

Marco Scarsini (Contact Author)

Luiss University Dipartimento di Economia e Finanza ( email )

Viale Romania 32
Rome, RM 00197
Italy

Tristan Tomala

HEC Paris - Economics & Decision Sciences ( email )

1 rue de la Liberation
Paris, 78351
France

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