On the Computational Complexity of Decision Problems About Multi-player Nash Equilibria

We study the computational complexity of decision problems about Nash equilibria in m-player games. Several such problems have recently been shown to be computationally equivalent to the decision problem for the existential theory of the reals, or stated in terms of complexity classes, \(\exists \mathbb {R}\)-complete, when \(m\ge 3\). We show that, unless they turn into trivial problems, they are \(\exists \mathbb {R}\)-hard even for 3-player zero-sum games.

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