Computing correlated equilibria of polynomial games via adaptive discretization

We construct a family of iterative discretization algorithms for computing sequences of finitely-supported ¿-correlated equilibria of
n
-player games with polynomial utility functions. These algorithms can be implemented efficiently using semidefinite programming and sum of squares techniques. They converge in the sense that they drive ¿ to zero in the limit as points are added to the discretization. We show how a natural discretization scheme proposed previously can be viewed as a limiting case of this new family of algorithms. Finally we provide a counterexample showing that this limiting case is singular, i.e., ¿ need not converge to zero.