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Polynomial computation of exact correlated equilibrium in compact games

Polynomial computation of exact correlated equilibrium in compact games Polynomial Computation of Exact Correlated Equilibrium in Compact Games ALBERT XIN JIANG and KEVIN LEYTON-BROWN Department of Computer Science, University of British Columbia In a landmark paper, Papadimitriou and Roughgarden described a polynomial-time algorithm ( œEllipsoid Against Hope ) for computing sample correlated equilibria of concisely-represented games. Recently, Stein, Parrilo and Ozdaglar showed that this algorithm can fail to nd an exact correlated equilibrium, but can be easily modi ed to e ƒciently compute approximate correlated equilibria. It remained an open problem to determine whether the algorithm can be modi ed to compute an exact correlated equilibrium. In a new paper, we showed that it can, presenting a variant of the Ellipsoid Against Hope algorithm that guarantees the polynomial-time identi cation of exact correlated equilibrium. Our new algorithm di €ers from the original primarily in its use of a separation oracle that produces cuts corresponding to pure-strategy pro les. As a result, we no longer face the numerical precision issues encountered by the original approach, and both the resulting algorithm and its analysis are considerably simpli ed. Our new separation oracle can be understood as a derandomization of Papadimitriou and Roughgarden ™s original separation oracle via the method http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png ACM SIGecom Exchanges Association for Computing Machinery

Polynomial computation of exact correlated equilibrium in compact games

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Publisher
Association for Computing Machinery
Copyright
Copyright © 2011 by ACM Inc.
ISSN
1551-9031
DOI
10.1145/1978721.1978723
Publisher site
See Article on Publisher Site

Abstract

Polynomial Computation of Exact Correlated Equilibrium in Compact Games ALBERT XIN JIANG and KEVIN LEYTON-BROWN Department of Computer Science, University of British Columbia In a landmark paper, Papadimitriou and Roughgarden described a polynomial-time algorithm ( œEllipsoid Against Hope ) for computing sample correlated equilibria of concisely-represented games. Recently, Stein, Parrilo and Ozdaglar showed that this algorithm can fail to nd an exact correlated equilibrium, but can be easily modi ed to e ƒciently compute approximate correlated equilibria. It remained an open problem to determine whether the algorithm can be modi ed to compute an exact correlated equilibrium. In a new paper, we showed that it can, presenting a variant of the Ellipsoid Against Hope algorithm that guarantees the polynomial-time identi cation of exact correlated equilibrium. Our new algorithm di €ers from the original primarily in its use of a separation oracle that produces cuts corresponding to pure-strategy pro les. As a result, we no longer face the numerical precision issues encountered by the original approach, and both the resulting algorithm and its analysis are considerably simpli ed. Our new separation oracle can be understood as a derandomization of Papadimitriou and Roughgarden ™s original separation oracle via the method

Journal

ACM SIGecom ExchangesAssociation for Computing Machinery

Published: Mar 1, 2011

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