States and microstates in a mean-field approach to the Minority Game and its generalizations

CARIDI I.

Mar del Plata, Pcia. de Buenos Aires, Argentina

Workshop; III Workshop on Dynamics of Social and Economic Systems; 2005

In this talk, we present a mean-field approach to the Minority Game, that allows us to reproduce the behavior of the model in the phase in which a so-called "dynamics of period two" is present. Our approach is based on the hypothesis that we can introduce states representative of the system, in such a form that averages over time can be replaced by averages over those states. Moreover, we define an ensemble of microstates and, thereafter, states compatible with the specifications of the game. In this work we explain in detail how to introduce these elements, and how to actually calculate the ensemble of states and microstates. We have developed one generalization of the Minority Game by introducing interactions among the agents. We also discuss and explain the adequate ensemble of states and microstates for that generalization.