Cahiers du CEREMADE

Unité Mixte de Recherche du C.N.R.S. N°7534
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 repeated games can be represented as colored sub-graphs of a de Bruijn graphs. 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. MSC 2000 Subject Classification: Primary 91A20. Secondary 91A18, 91A43. OR/MS subject classification: Primary: Games/group decisions, noncooperative. 2
A minority game with bounded recall
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