Quadratically optimal equilibrium points of weakly potential bi-matrix games

In this paper we show without using any fixed-point theorem argument, the existence of quadratically optimal equilibrium points of weakly potential bi-matrix games and quadratically optimal symmetric equilibrium points for those weakly potential square bi-matrix games which have potential matrices that are two-way matrices. The existence results are obtained as an optimal solution of a quadratic programming problem and hence constitute a refinement of the usual solution concepts for the subclass of games we consider.