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 (Formula Presented). 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. In particular, this implies that these problems are PPADꓵPLS-complete. As a corollary, we also obtain the following equivalence of complexity classes: CCLS = PPADꓵPLS.
| Original language | English |
|---|---|
| Pages (from-to) | STOC21-350-STOC21-404 |
| Journal | SIAM Journal on Computing |
| Volume | 55 |
| Issue number | 4 |
| DOIs | |
| State | Published - 2026 |
Keywords
- Nash equilibrium
- PLS
- PPAD
- computational complexity
- congestion games
- gradient descent
ASJC Scopus subject areas
- General Computer Science
- General Mathematics
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