Likelihood Equilibria in the Ising Game

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.