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The Payoff Region of a Strategic Game and Its Extreme Points

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  • Yu-Sung Tu
  • Wei-Torng Juang

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. "The Payoff Region of a Strategic Game and Its Extreme Points," Papers 1705.01454, arXiv.org, revised Aug 2018.
    • Handle: RePEc:arx:papers:1705.01454
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    3. Eddie Dekel & Jeffrey C. Ely & Okan Yilankaya, 2007. "Evolution of Preferences -super-1," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 74(3), pages 685-704.
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