Research Article
Nash equilibrium based fairness
@INPROCEEDINGS{10.1109/GAMENETS.2009.5137442, author={Hisao Kameda and Eitan Altman and Corinne Touati and Arnaud Legrand}, title={Nash equilibrium based fairness}, proceedings={1st International Conference on Game Theory for Networks}, publisher={IEEE}, proceedings_a={GAMENETS}, year={2009}, month={6}, keywords={Nash equilibrium Nash equilibrium based fairness Nash proportionate fairness flow control noncooperative game Pareto optimum and inefficiency power criterion.}, doi={10.1109/GAMENETS.2009.5137442} }- Hisao Kameda
Eitan Altman
Corinne Touati
Arnaud Legrand
Year: 2009
Nash equilibrium based fairness
GAMENETS
IEEE
DOI: 10.1109/GAMENETS.2009.5137442
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 ldquoNash equilibrium based fair.rdquo We further define a ldquoNash proportionately fairrdquo 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.
