Correlated Equilibria and Probabilistic Inference in Graphical Models

This paper explores the connection between belief inference and game-theoretic equilibria within the context of graphical models. While a lot of the work in graphical models for game theory has mirrored that in probabilistic graphical models, the paper also considers the opposite direction: Taking advantage of recent advances in equilibrium computation for probabilistic inference. In particular, the paper presents formulations of inference problems in Markov random fields as computation of equilibria in a certain class of game-theoretic graphical models. To do so, the paper introduces graphical multihypermatrix games (GMGs), a new class of graphical models for game theory that generalize graphical and polymatrix games. It also introduces graphical versions of potential games, which play a key role in the formulations, and presents results derived from the study of their properties. Finally, the paper includes a study of correlated equilibria in GMGs and provides both a characterization of the equilibria in such games and the design of a simple linear feasibility system for computing the equilibria based on the extension of a standard approach within the probabilistic and constraint graphical models community.