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Welfare-maximizing correlated equilibria using Kantorovich polynomials with sparsity

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Abstract

We provide motivations for the correlated equilibrium solution concept from the game-theoretic and optimization perspectives. We then propose an algorithm that computes \({\varepsilon}\) -correlated equilibria with global-optimal (i.e., maximum) expected social welfare for normal form polynomial games. We derive an infinite dimensional formulation of \({\varepsilon}\) -correlated equilibria using Kantorovich polynomials, and re-express it as a polynomial positivity constraint. We exploit polynomial sparsity to achieve a leaner problem formulation involving sum-of-squares constraints. By solving a sequence of semidefinite programming relaxations of the problem, our algorithm converges to a global-optimal \({\varepsilon}\) -correlated equilibrium. The paper ends with two numerical examples involving a two-player polynomial game, and a wireless game with two mutually-interfering communication links.

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  1. Department of Computing, Imperial College, South Kensington Campus, London, SW7 2AZ, UK

    Fook Wai Kong & Berç Rustem

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  1. Fook Wai Kong
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Kong, F.W., Rustem, B. Welfare-maximizing correlated equilibria using Kantorovich polynomials with sparsity. J Glob Optim 57, 251–277 (2013). https://doi.org/10.1007/s10898-012-9912-5

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