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. Our work improves the previously best known (0.38197 +)-approximation algorithm of Daskalakis, Mehta and Pa-padimitriou . First, we provide a… (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.