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Is there an algorithm that takes a game in normal form as input, and outputsa Nash equilibrium? If the payoffs are integers, the answer is yes, and lot ofwork has been done in its computational complexity. If the payoffs arepermitted to be real numbers, the answer is no, for continuity reasons. It isworthwhile to investigate the precise degree of non-computability (theWeihrauch degree), since knowing the degree entails what other approaches areavailable (eg, is there a randomized algorithm with positive success change?).The two player case has already been fully classified, but the multiplayer caseremains open and is addressed here. Our approach involves classifying thedegree of finding roots of polynomials, and lifting this to systems ofpolynomial inequalities via cylindrical algebraic decomposition.

The Weihrauch degree of finding Nash equilibria in multiplayer games