Welfare-maximizing correlated equilibria using Kantorovich polynomials with sparsity

  • Authors:

  • Fook Wai Kong;Berç Rustem

  • Affiliations:

  • Department of Computing, Imperial College, London, UK SW7 2AZ;Department of Computing, Imperial College, London, UK SW7 2AZ

  • Venue:
  • Journal of Global Optimization
  • Year:
  • 2013

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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.