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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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Submitted on : Sunday, July 3, 2016 - 4:21:56 AM
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Eitan Altman, Manjesh Kumar Hanawal Hanawal, Rajesh Sundaresan. Generalising diagonal strict concavity property for uniqueness of Nash equilibrium. Indian Journal of Pure and Applied Mathematics, Springer, 2016, 47 (2), pp.213-228. ⟨10.1007/s13226-016-0185-4⟩. ⟨hal-01340963⟩

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