Graphical Models for Game Theory

In this work, we introduce graphical modelsfor multi-player game theory, and give powerful algorithms for computing their Nash equilibria in certain cases. An n-player game is given by an undirected graph on n nodes and a set of n local matrices. The interpretation is that the payoff to player i is determined entirely by the actions of player i and his neighbors in the graph, and thus the payoff matrix to player i is indexed only by these players. We thus view the global n-player game as being composed of interacting local games, each involving many fewer players. Each player's action may have global impact, but it occurs through the propagation of local influences.Our main technical result is an efficient…