The Payoff Region of a Strategic Game and Its Extreme Points

Yu-Sung Tu and 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.

Date: 2017-05, Revised 2018-08
New Economics Papers: this item is included in nep-hpe
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Persistent link: https://EconPapers.repec.org/RePEc:arx:papers:1705.01454

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