Welfare-maximizing correlated equilibria using Kantorovich polynomials with sparsity

Fook Kong () and Berç Rustem ()

Journal of Global Optimization, 2013, vol. 57, issue 1, 277 pages

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. Copyright Springer Science+Business Media, LLC. 2013

Keywords: Game theory; Non-cooperative game; Correlated equilibrium; Global polynomial optimization; Sum of squares; Semidefinite programming; Wireless communication; 91A10; 91A80; 90C22; 11E25; 90B18 (search for similar items in EconPapers)
Date: 2013
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DOI: 10.1007/s10898-012-9912-5

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