Minority game: a mean-field-like approach

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 appropriate 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 ensemble averages over these states. Our results show a very good agreement with simulations results for most part of the informationally efficient phase.