Welfare-maximizing correlated equilibria using Kantorovich polynomials with sparsity |
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Authors: | Fook Wai Kong Berç Rustem |
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Institution: | 1. Department of Computing, Imperial College, South Kensington Campus, London, SW7 2AZ, UK
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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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