A Minority Game with Bounded Recall
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.