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Welfare-Maximizing Correlated Equilibria using Kantorovich Polynomials with Sparsity

Fook Wai Kong (fk07***at***doc.ic.ac.uk)
Berc Rustem (br***at***doc.ic.ac.uk)

Abstract: We propose an algorithm that computes the epsilon-correlated equilibria with global-optimal (i.e., maximum) expected social welfare for single stage polynomial games. We first derive an infinite-dimensional formulation of epsilon-correlated equilibria using Kantorovich polynomials and re-express it as a polynomial positivity constraint. In addition, we exploit polynomial sparsity to achieve a leaner problem formulation involving Sum-Of-Squares (SOS) constraints. We then give an asymptotic convergence proof and a dedicated sequential Semidefinite Programming(SDP) algorithm. We demonstrate the algorithm in a two-player polynomial game, and in a wireless game with two mutually-interfering communication links.

Keywords: Correlated equilibria, Noncooperative game, Semidefinite programming, Sum of squares, Polynomial optimization, Communication networks

Category 1: Other Topics (Game Theory )

Category 2: Linear, Cone and Semidefinite Programming (Semi-definite Programming )

Category 3: Global Optimization (Other )

Citation: Department of Computing, South Kensington Campus, Imperial College London SW7 2AZ, United Kingdom, September 2011

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Entry Submitted: 09/30/2011
Entry Accepted: 09/30/2011
Entry Last Modified: 05/15/2012

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