Let A be a m × n matrix which represents (exercise 3.253) the payoff function of a two-person zero-sum game in which player 1 has m pure strategies and player 2 has n strategies. Let Z be the convex hull of the columns of A, that is, Z = {z = Aq : q ˆˆ Δn-1}. Assume that v2 = 0.
Show that
1.

2.

3. There exists p* ˆˆ Δm-1 such that fp*(z) ‰¥ 0 for every z ˆˆ S.
4. v1 = 0 = v2.

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