Nash's Theorem proof in 2by2 games

[Bipolarity]

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

 

[mathman]

http://en.wikipedia.org/wiki/Nash_equilibrium#Proof_using_the_Kakutani_fixed_point_theorem

Did you google "nash's theorem proof"?

 

[Bipolarity]

Yep! The proofs that show up on google generalize it to 'n' players each having many strategies.

I was looking for a short proof on the simple case of 2by2 games with only 2 players. It should proof the existence of at least one Nash equilibrium.

BiP

 

[Bacle2]

Have you tried a search of the Minimax Theorem?

http://en.wikipedia.org/wiki/Minimax_theorem#Minimax_theorem