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arXiv · 1405.3322

Inapproximability of Nash Equilibrium

Aviad Rubinstein
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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.

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Aviad Rubinstein. 2014-05-13. Inapproximability of Nash Equilibrium. https://arxiv.org/abs/1405.3322

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