The professor told us today, that the set of optimal strategies of the row and column player in a two-player zero-sum game is convex, but he doesn't mention why that is.
What does it even mean that a set of strategies is convex?
Can somebody hint at me?
Edit: This basically means, I have to show that for any two optimal strategies a, b and $\lambda \in [0, 1]$:
$$\lambda a + (1 - \lambda)b$$
is also an optimal strategy.