Nash Propagation for Loopy Graphical Games

Abstract

We introduce NashProp, an iterative and local message-passing algo- rithm for computing Nash equilibria in multi-player games represented by arbitrary undirected graphs. We provide a formal analysis and exper- imental evidence demonstrating that NashProp performs well on large graphical games with many loops, often converging in just a dozen itera- tions on graphs with hundreds of nodes. NashProp generalizes the tree algorithm of (Kearns et al. 2001), and can be viewed as similar in spirit to belief propagation in probabilis- tic inference, and thus complements the recent work of (Vickrey and Koller 2002), who explored a junction tree approach. Thus, as for prob- abilistic inference, we have at least two promising general-purpose ap- proaches to equilibria computation in graphs.