Pure Nash equilibria: complete characterization of hard and easy graphical games

We consider the computational complexity of pure Nash equilibria in graphical games. It is known that the problem is NP-complete in general, but tractable (i.e., in P) for special classes of graphs such as those with bounded treewidth. It is then natural to ask: is it possible to characterize all tractable classes of graphs for this problem? In this work, we provide such a characterization for the case of bounded in-degree graphs, thereby resolving the gap between existing hardness and tractability results. In particular, we analyze the complexity of PURE-GG(C, -), the problem of deciding the existence of pure Nash equilibria in graphical games whose underlying graphs are restricted to class C. We prove that, under reasonable complexity theoretic assumptions, for every recursively enumerable class C of directed graphs with bounded indegree, PURE-GG(C, -) is in polynomial time if and only if the reduced graphs (the graphs resulting from iterated removal of sinks) of C have bounded tree...

• Type: Conference
• Year: 2010
• Where: ATAL
• Authors: Albert Xin Jiang, MohammadAli Safari
• Keywords: ATAL 2010, Computational Complexity, Graphical Games, Intelligent Agents, Pure Nash Equilibria