Journal of Optimization Theory and Applications

, Volume 153, Issue 1, pp 237–261

Computation of Correlated Equilibrium with Global-Optimal Expected Social Welfare

  • Fook Wai Kong
  • Polyxeni-Margarita Kleniati
  • Berç Rustem
Article

DOI: 10.1007/s10957-012-9988-6

Cite this article as:
Kong, F.W., Kleniati, PM. & Rustem, B. J Optim Theory Appl (2012) 153: 237. doi:10.1007/s10957-012-9988-6

Abstract

In this paper, we propose an algorithm which computes the correlated equilibrium with global-optimal (i.e., maximum) expected social welfare for single stage polynomial games. We first derive tractable primal/dual semidefinite programming (SDP) relaxations for an infinite-dimensional formulation of correlated equilibria. We give an asymptotic convergence proof, which ensures solving the sequence of relaxations leads to solutions that converge to the correlated equilibrium with the highest expected social welfare. Finally, we give a dedicated sequential SDP algorithm and demonstrate it in a wireless application with numerical results.

Keywords

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

Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  • Fook Wai Kong
    • 1
  • Polyxeni-Margarita Kleniati
    • 2
  • Berç Rustem
    • 1
  1. 1.Department of Computing, South Kensington CampusImperial CollegeLondonUK
  2. 2.Centre for Process Systems Engineering, South Kensington CampusImperial CollegeLondonUK