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Generalising diagonal strict concavity property for uniqueness of Nash equilibrium

Author

Listed:
  • Eitan Altman

    (INRIA Sophia Antipolis
    LINCS)

  • Manjesh Kumar Hanawal

    (Indian Institute of Technology Bombay)

  • Rajesh Sundaresan

    (Indian Institute of Science)

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.

Suggested Citation

  • Eitan Altman & Manjesh Kumar Hanawal & Rajesh Sundaresan, 2016. "Generalising diagonal strict concavity property for uniqueness of Nash equilibrium," Indian Journal of Pure and Applied Mathematics, Springer, vol. 47(2), pages 213-228, June.
    • Handle: RePEc:spr:indpam:v:47:y:2016:i:2:d:10.1007_s13226-016-0185-4
    DOI: 10.1007/s13226-016-0185-4
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    References listed on IDEAS

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    1. Oran Richman & Nahum Shimkin, 2007. "Topological Uniqueness of the Nash Equilibrium for Selfish Routing with Atomic Users," Mathematics of Operations Research, INFORMS, vol. 32(1), pages 215-232, February.
    2. Ramesh Johari & John N. Tsitsiklis, 2004. "Efficiency Loss in a Network Resource Allocation Game," Mathematics of Operations Research, INFORMS, vol. 29(3), pages 407-435, August.
    3. Ramesh Johari & John N. Tsitsiklis, 2009. "Efficiency of Scalar-Parameterized Mechanisms," Operations Research, INFORMS, vol. 57(4), pages 823-839, August.
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    Cited by:

    1. Shiva Raj Pokhrel & Carey Williamson, 2022. "A Game-Theoretic Rent-Seeking Framework for Improving Multipath TCP Performance," Future Internet, MDPI, vol. 14(9), pages 1-23, August.

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