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 subgraphs 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.
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