Stylized facts in minority games with memory: a new challenge

A finite memory is introduced in the score dynamics of Minority Games. As expected, this removes the dependence of the stationary state on the initial conditions. However, it also causes an unexpected increase of fluctuations in grand-canonical models for very large times. Current analytical methods are inadequate to solve this simple and natural extension. (C) 2004 Elsevier B.V. All rights reserved.