⎩ xp ∈ R

In the previous lecture we saw that there always exists a Nash equilibrium in two-player zero-sum games. Moreover, the equilibrium enjoys several attractive properties such as polynomial-time tractability, convexity of the equilibrium set, and uniqueness of players’ payoffs in all equilibria. In this lecture we explore whether we can generalize this theorem to multi-player zero-sum games. Before answering the question, let us formally define multi-player zero-sum games and generalize the concept of a Nash equilibrium from last lecture to these games.