Two-person nonzero-sum games and quadratic programming

AbstractIt is shown that a necessary and sufficient condition that a point be a Nash equilibrium point of a two-person, nonzero-sum game with a finite number of pure strategies is that the point be a solution of a single programming problem with linear constraints and a quadratic objective function that has a global maximum of zero. Every equilibrium point is a solution of this programming problem. For the case of a zero-sum game, the quadratic programming problem degenerates to the well-known dual linear programs associated with the game