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 maximization of the likelihood function of system configurations is presented. An equivalence of such likelihood equilibria to the competitive Bayes–Nash quantal response equilibria in the special case of self-consistent expectations of agents is established. It is shown that the same expectation equilibria can be obtained using the partition function formalism.