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The within groups and the between groups Myerson values

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  • González–Arangüena, E.
  • Manuel, C.
  • Owen, G.
  • del Pozo, M.

Abstract

In this paper we revisit the additive decomposition that Gómez et al. (2003) introduced for the Myerson value of a symmetric game when viewed as a centrality measure. First, we generalize this decomposition, extending it to general games. This approach permits us to look at the Myerson value of a player as a certain modulus of a two component vector. One of them, the within groups Myerson value, determines which part corresponds to the profit from the coalitions that a given player is in, whereas the other, the between groups Myerson value, evaluates the opportunities that player has as intermediary in the communication among others. These two values are then characterized using additivity and other properties related with previous interpretation: (A) The competitive advantages (or disadvantages) of a null player in a game with restrictions given by a graph (measured in terms of his Myerson value) are due to his ability to intermediate among the others. (B) In the same context, those players essential to coalitions that generate worth cannot obtain profit by intermediating. When restricted to certain symmetric games, the corresponding values can be considered as centrality measures, as they satisfy natural properties that reinforce this interpretation.

Suggested Citation

  • González–Arangüena, E. & Manuel, C. & Owen, G. & del Pozo, M., 2017. "The within groups and the between groups Myerson values," European Journal of Operational Research, Elsevier, vol. 257(2), pages 586-600.
    • Handle: RePEc:eee:ejores:v:257:y:2017:i:2:p:586-600
    DOI: 10.1016/j.ejor.2016.08.003
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    References listed on IDEAS

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    Cited by:

    1. Sylvain Béal & Florian Navarro, 2020. "Necessary versus equal players in axiomatic studies," Working Papers 2020-01, CRESE.
    2. Trudeau, Christian & Vidal-Puga, Juan, 2020. "Clique games: A family of games with coincidence between the nucleolus and the Shapley value," Mathematical Social Sciences, Elsevier, vol. 103(C), pages 8-14.
    3. Manuel, C. & Ortega, E. & del Pozo, M., 2020. "Marginality and Myerson values," European Journal of Operational Research, Elsevier, vol. 284(1), pages 301-312.
    4. C. Manuel & E. Ortega & M. del Pozo, 2023. "Marginality and the position value," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 31(2), pages 459-474, July.
    5. C. Manuel & D. Martín, 2021. "A value for communication situations with players having different bargaining abilities," Annals of Operations Research, Springer, vol. 301(1), pages 161-182, June.

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