Generalising diagonal strict concavity property for uniqueness of Nash equilibrium

Eitan Altman 1, 2, 3 Manjesh Kumar Hanawal 4 Rajesh Sundaresan 5
1 UCA - Université Côte d'Azur
2 LINCS - Laboratory of Information, Network and Communication Sciences
3 MAESTRO - Models for the performance analysis and the control of networks
CRISAM - Inria Sophia Antipolis - Méditerranée
4 IEOR - Industrial Engineering and Operations Research
5 ECE department - Department of Electrical Communication Engineering [Bangalore]
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 : Index Terms concave games diagonal strict concavity differential pricing Kelly mechanism Nash equilib- rium network resource allocation normalised Nash equilibrium
Type de document :
Article dans une revue
Indian Journal of Pure and Applied Mathematics, Indian National Science Academy, 2016, 47 (2), pp.213-228. 〈10.1007/s13226-016-0185-4〉
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Eitan Altman, Manjesh Kumar Hanawal, Rajesh Sundaresan. Generalising diagonal strict concavity property for uniqueness of Nash equilibrium. Indian Journal of Pure and Applied Mathematics, Indian National Science Academy, 2016, 47 (2), pp.213-228. 〈10.1007/s13226-016-0185-4〉. 〈hal-01340963〉

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