The Payoff Region of a Strategic Game and Its Extreme Points
For game theorists, this offers a new geometric tool to analyze payoff regions, though the results are theoretical and incremental in nature.
The paper introduces a novel approach using extreme points of non-convex sets to analyze the payoff region of finite strategic games, showing that noncooperative payoff subregions are non-strictly convex near boundary points and providing a simple proof method for Pareto and social efficiency results.
The range of a payoff function for an $n$-player finite strategic game is investigated using a novel approach, the notion of extreme points of a non-convex set. The shape of a noncooperative payoff region can be estimated using extreme points and supporting hyperplanes of the cooperative payoff region. A basic structural characteristic of a noncooperative payoff region is that any of its subregions must be non-strictly convex if the subregion contains a relative neighborhood of a point on its boundary. Besides, applying the properties of extreme points of a noncooperative payoff region is a simple and effective way to prove some results about Pareto efficiency and social efficiency in game theory.