1st International Conference on Game Theory for Networks

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
Hisao Kameda1,*, Eitan Altman2,*, Corinne Touati 3,*, Arnaud Legrand3,*
  • 1: Department of Computer Science, University of Tsukuba, Tsukuba Science City, Ibaraki, Japan.
  • 2: INRIA Sophia Antipolis, Sophia Antipolis, Cedex, France.
  • 3: CNRS and INRIA, LIG Laboratory, Montbonnot, France.
*Contact email: kameda@cs.tsukuba.ac.jp, Eitan.Altman@sophia.inria.fr, corinne.touati@imag.fr, arnaud.legrand}@imag.fr

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.