Settling the complexity of Nash equilibrium in congestion games

Yakov Babichenko; Aviad Rubinstein

doi:10.1145/3406325.3451039

Settling the complexity of Nash equilibrium in congestion games

Yakov Babichenko, Aviad Rubinstein

Data and Decision Sciences

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

Abstract

We consider (i) the problem of finding a (possibly mixed) Nash equilibrium in congestion games, and (ii) the problem of finding an (exponential precision) fixed point of the gradient descent dynamics of a smooth function f:[0,1]n ? R. We prove that these problems are equivalent. Our result holds for various explicit descriptions of f, ranging from (almost general) arithmetic circuits, to degree-5 polynomials. By a very recent result of [Fearnley et al., STOC 2021], this implies that these problems are PPAD PLS-complete. As a corollary, we also obtain the following equivalence of complexity classes: CCLS = PPAD PLS.

Original language	English
Title of host publication	STOC 2021 - Proceedings of the 53rd Annual ACM SIGACT Symposium on Theory of Computing
Editors	Samir Khuller, Virginia Vassilevska Williams
Pages	1426-1437
Number of pages	12
ISBN (Electronic)	9781450380539
DOIs	https://doi.org/10.1145/3406325.3451039
State	Published - 15 Jun 2021
Event	53rd Annual ACM SIGACT Symposium on Theory of Computing, STOC 2021 - Virtual, Online, Italy Duration: 21 Jun 2021 → 25 Jun 2021

Publication series

Name	Proceedings of the Annual ACM Symposium on Theory of Computing
ISSN (Print)	0737-8017

Conference

Conference	53rd Annual ACM SIGACT Symposium on Theory of Computing, STOC 2021
Country/Territory	Italy
City	Virtual, Online
Period	21/06/21 → 25/06/21

Keywords

Equilibrium computation
computational complexity
congestion games
gradient descent
potential games

ASJC Scopus subject areas

Software

Access to Document

10.1145/3406325.3451039

Cite this

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abstract = "We consider (i) the problem of finding a (possibly mixed) Nash equilibrium in congestion games, and (ii) the problem of finding an (exponential precision) fixed point of the gradient descent dynamics of a smooth function f:[0,1]n ? R. We prove that these problems are equivalent. Our result holds for various explicit descriptions of f, ranging from (almost general) arithmetic circuits, to degree-5 polynomials. By a very recent result of [Fearnley et al., STOC 2021], this implies that these problems are PPAD PLS-complete. As a corollary, we also obtain the following equivalence of complexity classes: CCLS = PPAD PLS.",

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Babichenko, Y & Rubinstein, A 2021, Settling the complexity of Nash equilibrium in congestion games. in S Khuller & VV Williams (eds), STOC 2021 - Proceedings of the 53rd Annual ACM SIGACT Symposium on Theory of Computing. Proceedings of the Annual ACM Symposium on Theory of Computing, pp. 1426-1437, 53rd Annual ACM SIGACT Symposium on Theory of Computing, STOC 2021, Virtual, Online, Italy, 21/06/21. https://doi.org/10.1145/3406325.3451039

Settling the complexity of Nash equilibrium in congestion games. / Babichenko, Yakov; Rubinstein, Aviad.
STOC 2021 - Proceedings of the 53rd Annual ACM SIGACT Symposium on Theory of Computing. ed. / Samir Khuller; Virginia Vassilevska Williams. 2021. p. 1426-1437 (Proceedings of the Annual ACM Symposium on Theory of Computing).

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

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Settling the complexity of Nash equilibrium in congestion games

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Keywords

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Access to Document

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