Computing Pure Nash Equilibria via Markov Random Fields
  In this paper we present a novel generic mapping between Graphical Games and Markov Random Fields so that pure Nash equilibria in the former can be found by statistical inference on the latter. Thus, the problem of deciding whether a graphical game has a pure Nash equilibrium, a well-known intractable problem, can be attacked by well-established algorithms such as Belief Propagation, Junction Trees, Markov Chain Monte Carlo and Simulated Annealing. Large classes of graphical games become thus tractable, including all classes already known, but also new classes such as the games with O(log n) treewidth. 
Constantinos Daskalakis