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Nash equilibrium based fairness

Author

Listed:
  • Hisao Kameda
  • Eitan Altman
  • Corinne Touati
  • Arnaud Legrand

Abstract

There are several approaches of sharing resources among users. There is a noncooperative approach wherein each user strives to maximize its own utility. The most common optimality notion is then the Nash equilibrium. Nash equilibria are generally Pareto inefficient. On the other hand, we consider a Nash equilibrium to be fair as it is defined in a context of fair competition without coalitions (such as cartels and syndicates). We show a general framework of systems wherein there exists a Pareto optimal allocation that is Pareto superior to an inefficient Nash equilibrium. We consider this Pareto optimum to be ‘Nash equilibrium based fair.’ We further define a ‘Nash proportionately fair’ Pareto optimum. We then provide conditions for the existence of a Pareto-optimal allocation that is, truly or most closely, proportional to a Nash equilibrium. As examples that fit in the above framework, we consider noncooperative flow-control problems in communication networks, for which we show the conditions on the existence of Nash-proportionately fair Pareto optimal allocations. Copyright Springer-Verlag 2012

Suggested Citation

  • Hisao Kameda & Eitan Altman & Corinne Touati & Arnaud Legrand, 2012. "Nash equilibrium based fairness," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 76(1), pages 43-65, August.
    • Handle: RePEc:spr:mathme:v:76:y:2012:i:1:p:43-65
    DOI: 10.1007/s00186-012-0389-2
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    References listed on IDEAS

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    1. Nash, John, 1950. "The Bargaining Problem," Econometrica, Econometric Society, vol. 18(2), pages 155-162, April.
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    Cited by:

    1. Hélène Le Cadre & Yuting Mou & Hanspeter Höschle, 2020. "Parametrized Inexact-ADMM to Span the Set of Generalized Nash Equilibria: A Normalized Equilibrium Approach," Working Papers hal-02925005, HAL.
    2. Zhaoyu Cao & Yucheng Zou & Xu Zhao & Kairong Hong & Yanwei Zhang, 2021. "Multidimensional Fairness Equilibrium Evaluation of Urban Housing Expropriation Compensation Based on VIKOR," Mathematics, MDPI, vol. 9(4), pages 1-26, February.
    3. Le Cadre, Hélène & Mou, Yuting & Höschle, Hanspeter, 2022. "Parametrized Inexact-ADMM based coordination games: A normalized Nash equilibrium approach," European Journal of Operational Research, Elsevier, vol. 296(2), pages 696-716.
    4. Kameda, Hisao, 2021. "Magnitude of inefficiency," European Journal of Operational Research, Elsevier, vol. 292(3), pages 1133-1145.

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