On two-player zero-sum games and conic linear programming

We show that strong duality for conic linear programming directly implies the minimax theorem for a wide class of infinite two-player zero-sum games. In fact, for every two-player zero-sum game with "cone-leveled" strategy sets, or more generally with strategy sets that can be written as unions of "cone-leveled" subsets, its game value and (approximate) optimal strategies can be calculated by solving a primal-dual pair of conic linear problems. The original result proven by von Neumann is therefore naturally generalized to the infinite-dimensional case, and a strong, rigorous connection between infinite two-player zero-sum games and mathematical programming is established.