Yakov Babichenko (IE, Technion)
Wednesday, 10.11.2021, 12:30
(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, Goldberg, Hollender, Savani ’21] this implies that these problems are PPAD \cap PLS-complete.
As a corollary, we also obtain the following equivalence of complexity classes:
CCLS = PPAD \cap PLS.
Joint work with Aviad Rubinstein.