Inapproximability of Nash Equilibrium

Abstract

We prove that finding an $\epsilon$-approximate Nash equilibrium is PPAD-complete for constant $\epsilon$ 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 $\epsilon$-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.

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