A Proof of Existence of Symmetric Equilibrium for Quadratically Symmetric bi-matrix games

We provide a proof of existence of symmetric equilibrium for quadratically similar symmetric bi-matrix games. We prove that any solution to a certain quadratic programming problem, is a symmetric equilibrium for the associated symmetric bi-matrix game. We use no more than the continuity of real-valued multi-variable quadratic functions and the mean value theorem for real-valued quadratic functions of a single variable. This proof can be easily understood by anyone who is familiar with a beginner's course on real analysis.