Nash equilibria in graphical games on trees revisited

Graphical games have been proposed as a game-theoretic model of large-scale distributed networks of non-cooperative agents. When the number of players is large, and the underlying graph has low degree, they provide a concise way to represent the players’ payoffs. It has recently been shown that the problem of finding Nash equilibria on a general degree-3 graphical game is complete for the complexity class PPAD, indicating that it is unlikely that there is any polynomial-time algorithm for this problem. We show here that in contrast, degree-2 graphical games are tractable. Our algorithm uses a dynamic-programming approach, which was introduced by Kearns, Littman and Singh in the context of graphical games on trees. The algorithm of Kearns et al. is a generic algorithm which can be used to compute all Nash equilibria. The running time is exponential, though approximate equilibria can be computed efficiently. Littman, Kearns and Singh proposed a modification to the generic algorithm...

• Type: Conference
• Year: 2006
• Where: SIGECOM
• Authors: Edith Elkind, Leslie Ann Goldberg, Paul W. Goldberg
• Keywords: Algorithm, Graphical Games, Nash Equilibria, SIGECOM 2006