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A weighted position value

Author

Listed:
  • Amandine Ghintran

    (CREUSET - Centre de Recherche Economique de l'Université de Saint-Etienne - UJM - Université Jean Monnet - Saint-Étienne)

Abstract

We provide a generalization of the position value (Meessen 1988) that allows players to benefit from transfers of worth by investing in communication links. The player who invests the most in a communication link obtains transfers of worth from the second one. We characterize this new allocation rule on the class of cycle free graphs by means of four axioms. The first two axioms, component efficiency and superfluous link property, are used to characterize the position value (Meessen (1988), Borm, Owen, and Tijs (1992)). Quasi-additivity is a weak version of the standard additivity axiom. The weighting axiom captures the fact that the allocation of players should be increasing with their level of investment.
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Suggested Citation

  • Amandine Ghintran, 2008. "A weighted position value," Post-Print hal-00332573, HAL.
    • Handle: RePEc:hal:journl:hal-00332573
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    Cited by:

    1. Jean-François Caulier & Michel Grabisch & Agnieszka Rusinowska, 2015. "An allocation rule for dynamic random network formation processes," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 60(2), pages 283-313, October.
    2. Niharika Kakoty & Surajit Borkotokey & Rajnish Kumar & Abhijit Bora, 2024. "Weighted Myerson value for Network games," Papers 2402.11464, arXiv.org.
    3. repec:hal:pseose:halshs-01207823 is not listed on IDEAS
    4. Navarro, Florian, 2020. "The center value: A sharing rule for cooperative games on acyclic graphs," Mathematical Social Sciences, Elsevier, vol. 105(C), pages 1-13.
    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.
    6. Alexander Mayer, 2018. "Luxembourg in the Early Days of the EEC: Null Player or Not?," Games, MDPI, vol. 9(2), pages 1-12, May.
    7. Elena C. Gavilán & Conrado M. Manuel & René Van Den Brink, 2022. "A Family of Position Values for Directed Communication Situations," Mathematics, MDPI, vol. 10(8), pages 1-19, April.
    8. Niharika Kakoty & Surajit Borkotokey & Rajnish Kumar & Abhijit Bora, 2023. "Weighted position value for Network games," Papers 2308.03494, arXiv.org.
    9. Julia Belau, 2018. "The class of ASN-position values," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 50(1), pages 65-99, January.
    10. Borkotokey, Surajit & Kumar, Rajnish & Sarangi, Sudipta, 2015. "A solution concept for network games: The role of multilateral interactions," European Journal of Operational Research, Elsevier, vol. 243(3), pages 912-920.

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