We formulate the problem of computing equilibria in multiplayer games represented by arbitrary undirected graphs as a constraint satisfaction problem and present two algorithms. The first is PureProp: an algorithm for computing approximate Nash equilibria in complete information one-shot games and approximate Bayes-Nash equilibria in one-shot games of incomplete information. PureProp unifies existing message-passing based algorithms for solving these classes of games. We also address repeated graphical games, and present a second algorithm, PureProp-R, for computing approximate Nash equilibria in these games.
