Polynomial-time computation of exact correlated equilibrium in compact games

In a landmark paper, Papadimitriou and Roughgarden [2008] described a polynomial-time algorithm (“Ellipsoid Against Hope”) for computing sample correlated equilibria of conciselyrepresented games. Recently, Stein, Parrilo and Ozdaglar [2010] showed that this algorithm can fail to find an exact correlated equilibrium, but can be easily modified to efficiently compute approximate correlated equilibria. Currently, it remains an open problem to determine whether the algorithm can be modified to compute an exact correlated equilibrium. We show that it can, presenting a variant of the Ellipsoid Against Hope algorithm that guarantees the polynomial-time identification of exact correlated equilibrium. Also, our algorithm is the first to tractably compute correlated equilibria with polynomial-sized supports; such correlated equilibria are more natural solutions than the mixtures of product distributions produced previously, and have several advantages including requiring fewer bits to...

• Type: Journal
• Year: 2011
• Where: SIGECOM
• Authors: Albert Xin Jiang, Kevin Leyton-Brown
• Keywords: Correlated Equilibria, Correlated Equilibrium, ECommerce, Polynomial Time Algorithm, SIGECOM 2011