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A General Framework for Computing Optimal Correlated Equilibria in Compact Games

(Extended Abstract)
  • Albert Xin Jiang
  • Kevin Leyton-Brown
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7090)

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.

Keywords

Nash Equilibrium Social Welfare Polynomial Time Pure Strategy Separation Problem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Albert Xin Jiang
    • 1
  • Kevin Leyton-Brown
    • 1
  1. 1.Department of Computer ScienceUniversity of British ColumbiaVancouverCanada

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