Statistical mechanics of the majority game

TL;DR

This paper models the majority game using statistical mechanics, analyzing its stationary states, phase diagram, and metastable states through theoretical calculations and numerical simulations.

Contribution

It introduces a statistical mechanics framework for the majority game, including phase diagram analysis and metastable state estimation.

Findings

Identification of stationary states as minima of a Hopfield-like Hamiltonian

Construction of the phase diagram including a retrieval phase

Estimation of metastable states using annealed approximation

Abstract

The majority game, modelling a system of heterogeneous agents trying to behave in a similar way, is introduced and studied using methods of statistical mechanics. The stationary states of the game are given by the (local) minima of a particular Hopfield like hamiltonian. On the basis of a replica symmetric calculations, we draw the phase diagram, which contains the analog of a retrieval phase. The number of metastable states is estimated using the annealed approximation. The results are confronted with extensive numerical simulations.