From naive to sophisticated behavior in multiagents-based financial market models

The behavior of physical complexity and mutual information function of the outcome of a model of heterogeneous, inductive rational agents inspired by the El Farol Bar problem and the Minority Game is studied. The first magnitude is a measure rooted in the Kolmogorov–Chaitin theory and the second a measure related to Shannonʹs information entropy. Extensive computer simulations were done, as a result of which, is proposed an ansatz for physical complexity of the type C(l)=lα and the dependence of the exponent α from the parameters of the model is established. The accuracy of our results and the relationship with the behavior of mutual information function as a measure of time correlation of agents choice are discussed.