Approximating nash equilibria in tree polymatrix games

Siddharth Barman; Katrina Ligett; Georgios Piliouras

doi:10.1007/978-3-662-48433-3_22

Approximating nash equilibria in tree polymatrix games

Siddharth Barman^*, Katrina Ligett, Georgios Piliouras

^*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

14 Scopus citations

Abstract

We develop a quasi-polynomial time Las Vegas algorithm for approximating Nash equilibria in polymatrix games over trees, under a mild renormalizing assumption. Our result, in particular, leads to an expected polynomial-time algorithm for computing approximate Nash equilibria of tree polymatrix games in which the number of actions per player is a fixed constant. Further, for trees with constant degree, the running time of the algorithm matches the best known upper bound for approximating Nash equilibria in bimatrix games (Lipton, Markakis, and Mehta 2003). Notably, this work closely complements the hardness result of Rubinstein (2015), which establishes the inapproximability of Nash equilibria in polymatrix games over constant-degree bipartite graphs with two actions per player.

Original language	American English
Title of host publication	Algorithmic Game Theory - 8th International Symposium, SAGT 2015
Editors	Martin Hoefer, Martin Hoefer
Publisher	Springer Verlag
Pages	285-296
Number of pages	12
ISBN (Print)	9783662484326
DOIs	https://doi.org/10.1007/978-3-662-48433-3_22
State	Published - 2015
Externally published	Yes
Event	8th International Symposium on Algorithmic Game Theory, SAGT 2015 - Saarbrucken, Germany Duration: 28 Sep 2015 → 30 Sep 2015

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	9347
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	8th International Symposium on Algorithmic Game Theory, SAGT 2015
Country/Territory	Germany
City	Saarbrucken
Period	28/09/15 → 30/09/15

Bibliographical note

Funding Information:
This work was supported by NSF grants CNS-0846025, CCF-1101470, CNS-1254169, SUTD grant SRG ESD 2015 097, along with a Microsoft Research Faculty Fellowship, a Google Faculty Research Award, a Linde/ SISL Postdoctoral Fellowship and a CMI Wally Baer and Jeri Weiss postdoctoral fellowship. Katrina Ligett gratefully acknowledges the support of the Charles Lee Powell Foundation. The bulk of the work was conducted while Georgios Piliouras was a postdoctoral scholar at Caltech.

Publisher Copyright:
© Springer International Publishing Switzerland 2015.

Access to Document

10.1007/978-3-662-48433-3_22

Cite this

Barman, S., Ligett, K., & Piliouras, G. (2015). Approximating nash equilibria in tree polymatrix games. In M. Hoefer, & M. Hoefer (Eds.), Algorithmic Game Theory - 8th International Symposium, SAGT 2015 (pp. 285-296). Article A22 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 9347). Springer Verlag. https://doi.org/10.1007/978-3-662-48433-3_22

Barman, Siddharth ; Ligett, Katrina ; Piliouras, Georgios. / Approximating nash equilibria in tree polymatrix games. Algorithmic Game Theory - 8th International Symposium, SAGT 2015. editor / Martin Hoefer ; Martin Hoefer. Springer Verlag, 2015. pp. 285-296 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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title = "Approximating nash equilibria in tree polymatrix games",

abstract = "We develop a quasi-polynomial time Las Vegas algorithm for approximating Nash equilibria in polymatrix games over trees, under a mild renormalizing assumption. Our result, in particular, leads to an expected polynomial-time algorithm for computing approximate Nash equilibria of tree polymatrix games in which the number of actions per player is a fixed constant. Further, for trees with constant degree, the running time of the algorithm matches the best known upper bound for approximating Nash equilibria in bimatrix games (Lipton, Markakis, and Mehta 2003). Notably, this work closely complements the hardness result of Rubinstein (2015), which establishes the inapproximability of Nash equilibria in polymatrix games over constant-degree bipartite graphs with two actions per player.",

author = "Siddharth Barman and Katrina Ligett and Georgios Piliouras",

note = "Funding Information: This work was supported by NSF grants CNS-0846025, CCF-1101470, CNS-1254169, SUTD grant SRG ESD 2015 097, along with a Microsoft Research Faculty Fellowship, a Google Faculty Research Award, a Linde/ SISL Postdoctoral Fellowship and a CMI Wally Baer and Jeri Weiss postdoctoral fellowship. Katrina Ligett gratefully acknowledges the support of the Charles Lee Powell Foundation. The bulk of the work was conducted while Georgios Piliouras was a postdoctoral scholar at Caltech. Publisher Copyright: {\textcopyright} Springer International Publishing Switzerland 2015.; 8th International Symposium on Algorithmic Game Theory, SAGT 2015 ; Conference date: 28-09-2015 Through 30-09-2015",

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Barman, S, Ligett, K & Piliouras, G 2015, Approximating nash equilibria in tree polymatrix games. in M Hoefer & M Hoefer (eds), Algorithmic Game Theory - 8th International Symposium, SAGT 2015., A22, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 9347, Springer Verlag, pp. 285-296, 8th International Symposium on Algorithmic Game Theory, SAGT 2015, Saarbrucken, Germany, 28/09/15. https://doi.org/10.1007/978-3-662-48433-3_22

Approximating nash equilibria in tree polymatrix games. / Barman, Siddharth; Ligett, Katrina; Piliouras, Georgios.
Algorithmic Game Theory - 8th International Symposium, SAGT 2015. ed. / Martin Hoefer; Martin Hoefer. Springer Verlag, 2015. p. 285-296 A22 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 9347).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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AU - Ligett, Katrina

AU - Piliouras, Georgios

N1 - Funding Information: This work was supported by NSF grants CNS-0846025, CCF-1101470, CNS-1254169, SUTD grant SRG ESD 2015 097, along with a Microsoft Research Faculty Fellowship, a Google Faculty Research Award, a Linde/ SISL Postdoctoral Fellowship and a CMI Wally Baer and Jeri Weiss postdoctoral fellowship. Katrina Ligett gratefully acknowledges the support of the Charles Lee Powell Foundation. The bulk of the work was conducted while Georgios Piliouras was a postdoctoral scholar at Caltech. Publisher Copyright: © Springer International Publishing Switzerland 2015.

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N2 - We develop a quasi-polynomial time Las Vegas algorithm for approximating Nash equilibria in polymatrix games over trees, under a mild renormalizing assumption. Our result, in particular, leads to an expected polynomial-time algorithm for computing approximate Nash equilibria of tree polymatrix games in which the number of actions per player is a fixed constant. Further, for trees with constant degree, the running time of the algorithm matches the best known upper bound for approximating Nash equilibria in bimatrix games (Lipton, Markakis, and Mehta 2003). Notably, this work closely complements the hardness result of Rubinstein (2015), which establishes the inapproximability of Nash equilibria in polymatrix games over constant-degree bipartite graphs with two actions per player.

AB - We develop a quasi-polynomial time Las Vegas algorithm for approximating Nash equilibria in polymatrix games over trees, under a mild renormalizing assumption. Our result, in particular, leads to an expected polynomial-time algorithm for computing approximate Nash equilibria of tree polymatrix games in which the number of actions per player is a fixed constant. Further, for trees with constant degree, the running time of the algorithm matches the best known upper bound for approximating Nash equilibria in bimatrix games (Lipton, Markakis, and Mehta 2003). Notably, this work closely complements the hardness result of Rubinstein (2015), which establishes the inapproximability of Nash equilibria in polymatrix games over constant-degree bipartite graphs with two actions per player.

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ER -

Barman S, Ligett K, Piliouras G. Approximating nash equilibria in tree polymatrix games. In Hoefer M, Hoefer M, editors, Algorithmic Game Theory - 8th International Symposium, SAGT 2015. Springer Verlag. 2015. p. 285-296. A22. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-662-48433-3_22

Approximating nash equilibria in tree polymatrix games

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