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We consider the problem of computing additively approximate Nash equilibria in non-cooperative two-player games. We provide a new polynomial time algorithm that achieves an approximation guarantee of 0.36392. We first provide a simpler algorithm, that achieves a 0.38197-approximation, which is exactly the same factor as the algorithm of Daskalakis, Mehta… (More)

Our main result is that every n-dimensional polytope can be described by at most 2n − 1 polynomial inequalities and, moreover, these polynomials can explicitly be constructed. For an n-dimensional pointed polyhedral cone we prove the bound 2n − 2 and for arbitrary polyhedra we get a constructible representation by 2n polynomial inequalities.

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