From naive to sophisticated behavior in multiagents based financial market models

We discuss the behavior of two magnitudes, physical complexity and mutual information function of the outcome of a model of heterogeneous, inductive rational agents inspired in the El Farol Bar problem and the Minority Game. The first is a measure rooted in Kolmogorov-Chaitin theory and the second one a measure related with information entropy of Shannon. We make extensive computer simulations, as result of which, we propose an ansatz for physical complexity and establish the dependence of exponent of that ansatz from the parameters of the model. We discuss the accuracy of our results and the relationship with the behavior of mutual information function as a measure of time correlations of agents choice.