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A Minority Game with Bounded Recall

CEREMADE, Université Paris Dauphine, Pl. du Marechal de Lattre de Tassigny, F-75775 Paris Cedex 16, France
Dipartimento di Scienze Economiche e Aziendali, LUISS, Viale Pola 12, I-00198 Roma, Italy, and HEC, Paris
CEREMADE, Université Paris Dauphine, Pl. du Marechal de Lattre de Tassigny, F-75775 Paris Cedex 16, France
renault{at}ceremade.dauphine.fr, http://www.ceremade.dauphine.fr/renault/
marco.scarsini{at}luiss.it, http://docenti.luiss.it/scarsini/
tomala{at}ceremade.dauphine.fr, http://www.ceremade.dauphine.fr/tomala/

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.

Key Words: folk theorem; de Bruijn sequence; imperfect monitoring; uniform equilibrium; public equilibrium; private equilibrium
History: Received: February 13, 2006; revision received: February 17, 2007;