triangle zero-sum games: three players 1, 2, 3 are pairwise engaged in two-player games, which need not be zero-sum. each player has the same strategy set in the two games s/he participates and needs to employ the same strategy in the two games. moreover, assume that, in every pure strategy profile, the sum of all players’ payoff is 0, i.e. that the overall game is zero-sum.