Technically, it's true that: -- The Von Neumann Min-Max Theorem is a special case of the existence of Nash Equilibria. -- Proving the original Min-Max Theorem

Technically, it's true that: -- The Von Neumann Min-Max Theorem is a special case of the existence of Nash Equilibria. -- Proving the original Min-Max Theorem isn't any any easier to do directly than is proving the existence of Nash Equilibria in general. That said, my dissertation was an extension of the Min-Max Theorem, and I basically didn't think about Nash Equilibria once the whole time I was working on it. THAT said, my dissertation was an independent proof of the theorem of Mertens and Neymann. Their proof seemed closer to the Fixed-Point Theorem kinds of techniques that Nash used. Anyhow, I'm pretty sure that Tom himself didn't engage in that kind of mathematics.