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arXiv · 1705.01454

The Payoff Region of a Strategic Game and Its Extreme Points

Yu-Sung Tu·Wei-Torng Juang
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Abstract

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.

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Yu-Sung Tu, Wei-Torng Juang. 2017-05-03. The Payoff Region of a Strategic Game and Its Extreme Points. https://arxiv.org/abs/1705.01454

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