English

Inapproximability of Nash Equilibrium

Computer Science and Game Theory 2016-09-14 v5

Abstract

We prove that finding an ϵ\epsilon-approximate Nash equilibrium is PPAD-complete for constant ϵ\epsilon and a particularly simple class of games: polymatrix, degree 3 graphical games, in which each player has only two actions. As corollaries, we also prove similar inapproximability results for Bayesian Nash equilibrium in a two-player incomplete information game with a constant number of actions, for relative ϵ\epsilon-Well Supported Nash Equilibrium in a two-player game, for market equilibrium in a non-monotone market, for the generalized circuit problem defined by Chen, Deng, and Teng [CDT'09], and for approximate competitive equilibrium from equal incomes with indivisible goods.

Keywords

Cite

@article{arxiv.1405.3322,
  title  = {Inapproximability of Nash Equilibrium},
  author = {Aviad Rubinstein},
  journal= {arXiv preprint arXiv:1405.3322},
  year   = {2016}
}

Comments

Fourth revision includes a new corollary for $\epsilon$-relative Nash equilibrium in two-player games, as well as new figures. Second revision includes new corollaries for Bayesian Nash equilibrium in two-player incomplete information games and for market equilibrium in a non-monotone market. arXiv admin note: text overlap with arXiv:1405.0524

R2 v1 2026-06-22T04:13:28.310Z