Minority games with finite score memory

We analyse grand canonical minority games with infinite and finite score memory and different updating timescales ( from 'on-line' games to 'batch' games) with various complementary methods, both analytical ( when possible) and numerical. We focus on the emergence of 'stylized facts' and on the production of exploitable information, as well as on the dynamic behaviour of the models. We find that no agent with finite score memory can be frozen in the steady state. As a consequence, traditional analytical tools do not allow for a complete characterization of the steady state and one must resort to Monte Carlo techniques for more insight.