Learning to coordinate in a complex and nonstationary world - art. no. 208701

We study analytically and by computer simulations a complex system of adapt ive agents with finite memory. Borrowing the framework of the minority game and using the replica formalism we show the existence of an equilibrium ph ase transition as a function of the ratio between the memory lambda and the learning rates Gamma of the agents. We show that, starting from a random c onfiguration, a dynamic phase transition also exists, which prevents agents from reaching optimal coordination. Furthermore, in a nonstationary enviro nment, we show by numerical simulations that the phase transition becomes d iscontinuous.