Non-equilibrium statistical mechanics of Minority Games

In this paper I give a brief introduction to a family of simple but non-trivial models designed to increase our understanding of collective processes in markets, the so-called Minority Games, and their non-equilibrium statistical mathematical analysis. Since the most commonly studied members of this family define disordered stochastic processes without detailed balance, the canonical technique for finding exact solutions is found to be generating functional analysis a la De Dominicis, as originally developed in the spin-glass community.