@inproceedings{7abf38318bea414db62c4ee506d48684,
title = "Settling the complexity of Nash equilibrium in congestion games",
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.",
keywords = "Equilibrium computation, computational complexity, congestion games, gradient descent, potential games",
author = "Yakov Babichenko and Aviad Rubinstein",
note = "Publisher Copyright: {\textcopyright} 2021 ACM.; 53rd Annual ACM SIGACT Symposium on Theory of Computing, STOC 2021 ; Conference date: 21-06-2021 Through 25-06-2021",
year = "2021",
month = jun,
day = "15",
doi = "https://doi.org/10.1145/3406325.3451039",
language = "الإنجليزيّة",
series = "Proceedings of the Annual ACM Symposium on Theory of Computing",
pages = "1426--1437",
editor = "Samir Khuller and Williams, {Virginia Vassilevska}",
booktitle = "STOC 2021 - Proceedings of the 53rd Annual ACM SIGACT Symposium on Theory of Computing",
}