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Necessary players, Myerson fairness and the equal treatment of equals

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Abstract

This article addresses linear sharing rules on transferable utility games (TU-games) with various structures, namely communication structures and conference structures as defined by Myerson in two papers (Myerson in Mathematics of Operations Research 2:225–229, 1977; Myerson in International Journal of Game Theory 9:169–182, 1980). Here, using matrix expressions, we rewrite those sharing rules. With this presentation we identify the close relationship between the fairness property and an equal treatment of necessary players axiom. Moreover, we show that the latter is implied by the equal treatment of equals, linking the fairness property to the notion of equality.

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Notes

  1. The propinquity between these frameworks is explored in Algaba et al. (2004).

  2. The correct notation for \(g{\setminus }\{i,j\}\) would be \(g{\setminus }\{\{i,j\}\}\). However, for ease of reading, we decided to simplify the notation.

  3. A third appearance of the fairness axiom is also defined for union stable systems by Algaba et al. (2001) to define the Myerson value for union stable systems.

  4. Since we deal with a finite number of coalitions, the characteristic function v can also be written in a finite vector form. Each element of the vector is the worth of the corresponding coalition. In the following we use v to denote the function or the vector. Further down we also use v / g the same way.

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Authors and Affiliations

  1. Laboratoire LEM UMR 9221, Université de Lille, Maison de la Recherche Domaine universitaire du Pont de Bois, B.P. 60149, 59653, Villeneuve d’Ascq Cedex, France

    Florian Navarro

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  1. Florian Navarro
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Correspondence to Florian Navarro.

Additional information

This article is part of my Ph.D. dissertation that is conducted under the supervision of Pr. Gérard Hamiache. I am grateful for his guidance and precious advice.

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Navarro, F. Necessary players, Myerson fairness and the equal treatment of equals. Ann Oper Res 280, 111–119 (2019). https://doi.org/10.1007/s10479-018-3055-0

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  • DOI: https://doi.org/10.1007/s10479-018-3055-0

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