A general framework for computing optimal correlated equilibria in compact games

  • Authors:

  • Albert Xin Jiang;Kevin Leyton-Brown

  • Affiliations:

  • Department of Computer Science, University of British Columbia, Vancouver, Canada;Department of Computer Science, University of British Columbia, Vancouver, Canada

  • Venue:
  • WINE'11 Proceedings of the 7th international conference on Internet and Network Economics
  • Year:
  • 2011

Quantified Score

Hi-index 0.00

Visualization

Abstract

We analyze the problem of computing a correlated equilibrium that optimizes some objective (e.g., social welfare). Papadimitriou and Roughgarden [2008] gave a sufficient condition for the tractability of this problem; however, this condition only applies to a subset of existing representations. We propose a different algorithmic approach for the optimal CE problem that applies to all compact representations, and give a sufficient condition that generalizes that of Papadimitriou and Roughgarden [2008]. In particular, we reduce the optimal CE problem to the deviation −adjusted social welfare problem , a combinatorial optimization problem closely related to the optimal social welfare problem. This framework allows us to identify new classes of games for which the optimal CE problem is tractable; we show that graphical polymatrix games on tree graphs are one example. We also study the problem of computing the optimal coarse correlated equilibrium , a solution concept closely related to CE. Using a similar approach we derive a sufficient condition for this problem, and use it to prove that the problem is tractable for singleton congestion games.