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Nash Equilibrium Based Fairness

Hisao Kameda 1 Eitan Altman 2 Corinne Touati 3 Arnaud Legrand 3
2 MAESTRO - Models for the performance analysis and the control of networks
CRISAM - Inria Sophia Antipolis - Méditerranée
3 MESCAL - Middleware efficiently scalable
Inria Grenoble - Rhône-Alpes, LIG [2007-2015] - Laboratoire d'Informatique de Grenoble [2007-2015]
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.
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Contributor : Corinne Touati <>
Submitted on : Thursday, October 18, 2012 - 10:58:46 AM
Last modification on : Wednesday, October 14, 2020 - 4:24:30 AM

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Hisao Kameda, Eitan Altman, Corinne Touati, Arnaud Legrand. Nash Equilibrium Based Fairness. Mathematical Methods of Operations Research, Springer Verlag, 2012, 76 (1), ⟨10.1007/s00186-012-0389-2⟩. ⟨hal-00743123⟩



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