Statistical mechanics of systems with heterogeneous agents: Minority Games

TL;DR

This paper analyzes a model of heterogeneous agents using statistical mechanics, revealing that the system's stationary state aligns with a solvable disordered spin model, distinct from the Nash equilibrium.

Contribution

It introduces an analytical approach linking a game theoretical model to a disordered spin system, highlighting differences from Nash equilibrium through replica symmetry analysis.

Findings

Stationary state matches the ground state of a disordered spin model.

Nash equilibrium exhibits replica symmetry breaking.

Numerical results confirm analytical predictions.

Abstract

We study analytically a simple game theoretical model of heterogeneous interacting agents. We show that the stationary state of the system is described by the ground state of a disordered spin model which is exactly solvable within the simple replica symmetric ansatz. Such a stationary state differs from the Nash equilibrium where each agent maximizes her own utility. The latter turns out to be characterized by a replica symmetry broken structure. Numerical results fully agree with our analytic findings.