TY - GEN

T1 - Settling the complexity of Nash equilibrium in congestion games

AU - Babichenko, Yakov

AU - Rubinstein, Aviad

N1 - Publisher Copyright:
© 2021 ACM.

PY - 2021/6/15

Y1 - 2021/6/15

N2 - 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.

AB - 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.

KW - Equilibrium computation

KW - computational complexity

KW - congestion games

KW - gradient descent

KW - potential games

UR - http://www.scopus.com/inward/record.url?scp=85102664314&partnerID=8YFLogxK

U2 - 10.1145/3406325.3451039

DO - 10.1145/3406325.3451039

M3 - ???researchoutput.researchoutputtypes.contributiontobookanthology.conference???

AN - SCOPUS:85102664314

T3 - Proceedings of the Annual ACM Symposium on Theory of Computing

SP - 1426

EP - 1437

BT - STOC 2021 - Proceedings of the 53rd Annual ACM SIGACT Symposium on Theory of Computing

A2 - Khuller, Samir

A2 - Williams, Virginia Vassilevska

T2 - 53rd Annual ACM SIGACT Symposium on Theory of Computing, STOC 2021

Y2 - 21 June 2021 through 25 June 2021

ER -