Nash equilibrium based fairness

Authors:
Hisao Kameda;Eitan Altman;Corinne Touati;Arnaud Legrand
Affiliations:
Department of Computer Science, University of Tsukuba, Tsukuba Science City, Ibaraki, Japan;INRIA Sophia Antipolis, Sophia Antipolis, Cedex, France;CNRS and INRIA, LIG Laboratory, Montbonnot, France;CNRS and INRIA, LIG Laboratory, Montbonnot, France
Venue:
GameNets'09 Proceedings of the First ICST international conference on Game Theory for Networks
Year:
2009

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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.