# Nash's Theorem proof in 2by2 games

According to Nash's Theorem, every game has at least one Nash Equilibrium, whether that be a pure strategy or a mixed strategy Nash equilibrium. However, I have not been able to find a proof for the theorem.

I am looking for a proof of the theorem in 2by2 games involving simultaneous strategies. Perhaps someone here knows good places where these proofs can be found? I googled but most seem to explain the theorem rather superficially without a rigorous mathematical approach.

Thanks!

BiP