On non-ergodic phases in Minority Games

In the first part of this review, we survey the known analytic results regarding the non-ergodic phase of standard Minority Games. Such phases are characterized by the fact that, at odds with ergodic regimes, the steady state properties of the game (e.g. the volatility) depend both on the initial conditions chosen for the agents' learning process as well as on the learning rate. Secondly, we present a discussion of the effects of finite-memory learning, which lifts the non-ergodicity, in the context of spherical Minority Games.