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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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    1. Winter, Eyal, 1992. "The consistency and potential for values of games with coalition structure," Games and Economic Behavior, Elsevier, vol. 4(1), pages 132-144, January.
    2. Herings, P. Jean Jacques & van der Laan, Gerard & Talman, Dolf, 2008. "The average tree solution for cycle-free graph games," Games and Economic Behavior, Elsevier, vol. 62(1), pages 77-92, January.
    3. André Casajus, 2009. "Networks and outside options," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 32(1), pages 1-13, January.
    4. Jackson, Matthew O. & Wolinsky, Asher, 1996. "A Strategic Model of Social and Economic Networks," Journal of Economic Theory, Elsevier, vol. 71(1), pages 44-74, October.
    5. van den Nouweland, Anne & Borm, Peter & Tijs, Stef, 1992. "Allocation Rules for Hypergraph Communication Situations," International Journal of Game Theory, Springer;Game Theory Society, vol. 20(3), pages 255-268.
    6. González–Arangüena, Enrique & Manuel, Conrado Miguel & del Pozo, Mónica, 2015. "Values of games with weighted graphs," European Journal of Operational Research, Elsevier, vol. 243(1), pages 248-257.
    7. Hart, Sergiu & Mas-Colell, Andreu, 1989. "Potential, Value, and Consistency," Econometrica, Econometric Society, vol. 57(3), pages 589-614, May.
    8. Béal, Sylvain & Rémila, Eric & Solal, Philippe, 2010. "Rooted-tree solutions for tree games," European Journal of Operational Research, Elsevier, vol. 203(2), pages 404-408, June.
    9. Roger B. Myerson, 1977. "Graphs and Cooperation in Games," Mathematics of Operations Research, INFORMS, vol. 2(3), pages 225-229, August.
    10. Gomez, Daniel & Gonzalez-Aranguena, Enrique & Manuel, Conrado & Owen, Guillermo & del Pozo, Monica & Tejada, Juan, 2003. "Centrality and power in social networks: a game theoretic approach," Mathematical Social Sciences, Elsevier, vol. 46(1), pages 27-54, August.
    11. Calvo, Emilio & Lasaga, Javier & van den Nouweland, Anne, 1999. "Values of games with probabilistic graphs," Mathematical Social Sciences, Elsevier, vol. 37(1), pages 79-95, January.
    12. E. Algaba & J. M. Bilbao & P. Borm & J. J. López, 2001. "The Myerson value for union stable structures," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 54(3), pages 359-371, December.
    13. Gómez, D. & González-Arangüena, E. & Manuel, C. & Owen, G., 2008. "A value for generalized probabilistic communication situations," European Journal of Operational Research, Elsevier, vol. 190(2), pages 539-556, October.
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    Cited by:

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    3. Sylvain Béal & Florian Navarro, 2020. "Necessary versus equal players in axiomatic studies," Post-Print hal-03252179, HAL.
    4. Manuel, C. & Ortega, E. & del Pozo, M., 2020. "Marginality and Myerson values," European Journal of Operational Research, Elsevier, vol. 284(1), pages 301-312.
    5. 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.

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