A mixed graphG π contains both undirected edges and directed arcs. Ak-coloring ofG π is an assignment to its vertices of integers not exceedingk (also called colors) so that the endvertices of an edge have different colors and the tail of any arc has a smaller color than its head. The...

It is well known that the set of correlated equilibrium distributions of an n-player noncooperative game is a convex polytope that includes all the Nash equilibrium distributions. We demonstrate an elementary yet surprising result: the Nash equilibria all lie on the boundary of the polytope....