We prove a generalization of von Neumann’s minmax theorem to the class of separable multiplayer zerosum games, introduced in [Bregman and Fokin 1998]. These games are polymatrix—that is, graphical games in which every edge is a two-player game between its endpoints—in which every outcome has zero total sum of players’ payoffs. Our generalization of the minmax theorem implies convexity of equili...

Strictly competitive games are a class of 2-player games often quoted in the literature to be a proper generalization of zero-sum games. Other times it is claimed, e.g. by Aumann, that strictly competitive games are only payoff transformations of zero-sum games. But to the best of our knowledge there is no proof of such claim. We shed light to this point of confusion in the literature, showing ...