Minority Game: a mean-field-like approach

Abstract

We calculate the standard deviation of (N1-N0), the difference of the number of agents choosing between the two alternatives of the minority game. Our approach is based on two approximations: we use the whole set of possible strategies, rather than only those distributed between the agents involved in a game; moreover, we assume that a period-two dynamics discussed by previous authors is appropiate within the range of validity of our work. With these approximations we introduce a set of states of the system, and are able to replace time averages by ensamble averages over these states. Our results show very good agreement with simulations results for most part of the informationally efficient phase.