GENERALISING DIAGONAL STRICT CONCAVITY PROPERTY FOR UNIQUENESS OF NASH EQUILIBRIUM

被引：4

作者：

Altman, Eitan ^{[1
,2
]}

Hanawal, Manjesh Kumar ^{[3
]}

Sundaresan, Rajesh ^{[4
]}

机构：

[1] INRIA Sophia Antipolis, 2004 Route Lucioles BP 93, F-06902 Sophia Antipolis, France

[2] LINCS, 23 Ave Italie, F-75013 Paris, France

[3] Indian Inst Technol, Ind Engn & Operat Res, Mech Engn Bldg, Bombay 400076, Maharashtra, India

[4] Indian Inst Sci, Dept Elect Commun Engn, Bangalore 560012, Karnataka, India

来源：

INDIAN JOURNAL OF PURE & APPLIED MATHEMATICS | 2016年 / 47卷 / 02期

关键词：

Concave games; diagonal strict concavity; differential pricing; Kelly mechanism; Nash equilibrium; network resource allocation; normalised Nash equilibrium; RESOURCE-ALLOCATION GAME; EFFICIENCY-LOSS; POWER-CONTROL;

D O I：

10.1007/s13226-016-0185-4

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we extend the notion of diagonally strictly concave functions and use it to provide a sufficient condition for uniqueness of Nash equilibrium in some concave games. We then provide an alternative proof of the existence and uniqueness of Nash equilibrium for a network resource allocation game arising from the so-called Kelly mechanism by verifying the new sufficient condition. We then establish that the equilibrium resulting from the differential pricing in the Kelly mechanism is related to a normalised Nash equilibrium of a game with coupled strategy space.

引用

页码：213 / 228

页数：16

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