Abstract:Given a rank-1 bimatrix game (A, B), i.e., where rank(A+ B) = 1, we construct a suitable linear subspace of the rank-1 game space and show that this subspace is homeomorphic to its Nash equilibrium correspondence. Using this homeomorphism, we give the first polynomial time algorithm for computing an exact Nash equilibrium of a rank-1 bimatrix game. This settles an open question posed in [8,21]. In addition, we give a novel algorithm to enumerate all the Nash equilibria of a rank-1 game and show that a similar … Show more
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