Non-equilibrium statistical mechanics of Minority Games

TL;DR

This paper introduces the non-equilibrium statistical mechanics framework for analyzing Minority Games, a class of models for collective market behavior, using advanced generating functional techniques from spin-glass theory.

Contribution

It applies generating functional analysis to disordered stochastic processes in Minority Games, advancing understanding of their non-equilibrium dynamics.

Findings

Analytical solutions for Minority Games using generating functionals

Insights into collective market phenomena from non-equilibrium models

Extension of spin-glass methods to economic models

Abstract

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.