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A weighted position value

Author

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  • Amandine Ghintran

    (Óbuda University)

Abstract

We provide a generalization of the position value (Meessen 1988) that allows players to benefit from transfers of worth by investing in their communication links. The player who invests the most in a communication link obtains a compensation from the second one. We characterize this new allocation rule on the class of communication situations with cycle-free graphs by means of six axioms. The first two axioms, component efficiency and superfluous link property, are used to characterize the position value (Borm, Owen, and Tijs (1992)). Quasi-additivity is a weak version of the standard additivity axiom. Link decomposability captures the fact that the insurance system only allows compensations between players who share a link. Weak positivity states that if the communicative strength of a link is non null, its adjacent players cannot obtain a null payoff. Finally, weak power inversion reflects the compensation mechanism.

Suggested Citation

  • Amandine Ghintran, 2010. "A weighted position value," Working Paper Series 1008, Óbuda University, Keleti Faculty of Business and Management.
    • Handle: RePEc:pkk:wpaper:1008.rdf
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    References listed on IDEAS

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    1. Marco Slikker, 2005. "A characterization of the position value," International Journal of Game Theory, Springer;Game Theory Society, vol. 33(4), pages 505-514, November.
    2. Chun, Youngsub, 1991. "On the Symmetric and Weighted Shapley Values," International Journal of Game Theory, Springer;Game Theory Society, vol. 20(2), pages 183-190.
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    6. Borm, P.E.M. & Owen, G. & Tijs, S.H., 1992. "On the position value for communication situations," Other publications TiSEM 5a8473e4-1df7-42df-ad53-f, Tilburg University, School of Economics and Management.
    7. Guillaume Haeringer, 1999. "Weighted Myerson Value," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 1(02), pages 187-192.
    8. Marco Slikker & Anne van den Nouweland, 2000. "Communication situations with asymmetric players," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 52(1), pages 39-56, September.
    9. Ehud Kalai & Dov Samet, 1983. "On Weighted Shapley Values," Discussion Papers 602, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    10. Jean J. M. Derks & Hans H. Haller, 1999. "Null Players Out? Linear Values For Games With Variable Supports," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 1(03n04), pages 301-314.
    11. Guillermo Owen, 1968. "Communications to the Editor--A Note on the Shapley Value," Management Science, INFORMS, vol. 14(11), pages 731-731, July.
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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. 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.
    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. Niharika Kakoty & Surajit Borkotokey & Rajnish Kumar & Abhijit Bora, 2023. "Weighted position value for Network games," Papers 2308.03494, arXiv.org.
    6. 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.
    7. 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.
    8. 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.
    9. Alexander Mayer, 2018. "Luxembourg in the Early Days of the EEC: Null Player or Not?," Games, MDPI, vol. 9(2), pages 1-12, May.

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    Keywords

    Weighted position value; Monotonicity;

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