The Complexity of Exact and Approximate Nash Equilibria in Anonymous Games

We prove that, for every fixed rational $c>0$, computing a $2^{-n^c}$-approximate Nash equilibrium in an $n$-player two-strategy anonymous game is $\mathsf{PPAD}$-complete. This holds even when one strategy always pays $1/2$ and, for all but two players, the other is constant outside at most five op