Generalising diagonal strict concavity property for uniqueness of Nash equilibrium

Eitan Altman (), Manjesh Kumar Hanawal () and Rajesh Sundaresan ()
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Eitan Altman: INRIA Sophia Antipolis
Manjesh Kumar Hanawal: Indian Institute of Technology Bombay
Rajesh Sundaresan: Indian Institute of Science

Indian Journal of Pure and Applied Mathematics, 2016, vol. 47, issue 2, 213-228

Abstract: Abstract 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.

Keywords: Concave games; diagonal strict concavity; differential pricing; Kelly mechanism; Nash equilibrium; network resource allocation; normalised Nash equilibrium (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s13226-016-0185-4

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