Self-Excited Ising Game

TL;DR

This paper investigates how self-excited activity spillover influences the dynamics of a noisy Ising game on a complete graph, revealing accelerated relaxation and transitions between metastable states.

Contribution

It introduces the concept of activity spillover effects in the Ising game and analyzes their impact on system dynamics using master equations.

Findings

Activity spillover accelerates relaxation to equilibrium.

Transitions between metastable states occur faster with spillover.

The study bridges economics and statistical physics through this model.

Abstract

Effects of dynamical activity spillover in a noisy binary choice game (Ising game) on a complete graph are studied. Binary choice games are very important for both economics and statistical physics playing a role of the bridge between these two fields. In this paper we investigate the effects of self-excited activity induced by activity spillover on relaxation to equilibria and transitions between metastable equilibria at finite times. Using the formalism of master equations we show that both relaxation and interequilibria transitions at finite time are accelerated by the effects of activity spillover.