We prove that finding the solution of two player Nash Equilibrium is PPAD-complete.

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We prove that computing a Nash equilibrium in a 3-player
game is PPAD-complete, solving a problem left open in our recent result on the complexity of Nash equilibria.

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We introduce some operators defining new complexity classes from existing ones in the Blum-Shub-Smale theory of computation over the reals. Each one of these operators is defined with the help of a quantifier differing from the usual ones, $\forall$ and $\exists$, and yet having a precise geometric meaning. Our agenda ... more >>>