Without looking it up, I don't think the timing was right. He once said his work during WW2 was one of the highlights o his life, but while I forget the details, I think it was conventional economies rather than the strategy stuff for which he became famous.
Wikipedia says the von Neumann version of the NashEq was published in 1944 when Schelling was just graduating. And also that Cournot published a version in 1838...
-- 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.
