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.

• Type: Conference
• Year: 2008
• Where: CDC
• Authors: Noah D. Stein, Asuman E. Ozdaglar, Pablo A. Parrilo
• Keywords: CDC 2008, Control Systems, Iterative Discretization Algorithms, Natural Discretization Scheme, finitely-supported Correlated Equilibria