The Payoff Region of a Strategic Game and Its Extreme Points

The range of a payoff function in an n-player finite strategic game is investigated using a novel approach, the notion of extreme points of a nonconvex set. A basic structural characteristic of a noncooperative payoff region is that any subregion must be non-strictly convex if it contains a relative neighborhood of a boundary point of the noncooperative payoff region. This can be proved efficiently in terms of its extreme points. Besides, applying the properties of extreme points of noncooperative payoff regions is a simple and efficient way to prove some results about Pareto analysis in game theory.