Likelihood Equilibria in the Ising Game

TL;DR

This paper explores the static equilibria of the Ising game on various graph structures, linking likelihood maximization to Bayesian equilibrium concepts and partition functions, providing new insights into system behavior.

Contribution

It establishes the equivalence between likelihood equilibria and Bayesian Nash equilibria in the Ising game, connecting statistical mechanics with game theory.

Findings

Likelihood equilibria correspond to Bayesian Nash equilibria with consistent expectations.

Equilibria can be derived from the system's partition function.

The approach applies to complete and random graph structures.

Abstract

A description of static equilibria in the noisy binary choice (Ising) game on complete and random graphs resulting from maximisation of the likelihood of system configurations is presented. An equivalence of such likelihood equilibria to the competitive Bayes-Nash quantal response expectation equilibria in the special case of consistent agents expectations is established. It is shown that the same likelihood equilibria are obtained by considering the system's partition function.