Minority Game: a mean-field-like approach

TL;DR

This paper presents a mean-field-like analytical approach to the minority game, calculating the standard deviation of agents' choices and showing good agreement with simulations in the efficient phase.

Contribution

It introduces a novel approximation method using the entire strategy set and a period-two dynamics assumption to analyze the minority game.

Findings

Accurately predicts the standard deviation in the efficient phase.

Shows strong agreement with simulation results.

Provides a new analytical framework for the minority game.

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.