Generalising diagonal strict concavity property for uniqueness of Nash equilibrium

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.
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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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