A Simple Proof of Existence of Symmetric Equilibrium for Symmetric Bi-matrix games: A Quadratic Programming Approach

Abstract

We provide a proof of existence of symmetric equilibrium for symmetric bi-matrix games, a result implied by a more general result that was proved by John Nash. Our proof, unlike the original proof due to Nash, does not appeal to the Brouwer fixed point theorem. We prove that any solution to a certain specific quadratic programming problem, is a symmetric equilibrium for the associated symmetric bi-matrix game.