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A probabilistic position value

Author

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  • Amandine Ghintran

    (GATE Lyon Saint-Étienne - Groupe d'Analyse et de Théorie Economique Lyon - Saint-Etienne - ENS de Lyon - École normale supérieure de Lyon - UL2 - Université Lumière - Lyon 2 - UCBL - Université Claude Bernard Lyon 1 - Université de Lyon - UJM - Université Jean Monnet - Saint-Étienne - CNRS - Centre National de la Recherche Scientifique, EQUIPPE - Economie Quantitative, Intégration, Politiques Publiques et Econométrie - Université de Lille, Sciences et Technologies - Université de Lille, Sciences Humaines et Sociales - PRES Université Lille Nord de France - Université de Lille, Droit et Santé)

  • Enrique Gonzalez-Aranguena

    (departemento de Estadìstica e Investigaciòn Operativa III - departemento de Estadìstica e Investigaciòn Operativa III - UEM - Universidad Europea de Madrid = European University of Madrid)

  • Conrado Manuel

    (Trier University)

Abstract

In this article, we generalize the position value, defined by Meessen (1988) for the class of deterministic communication situations, to the class of generalized probabilistic com- munication situations (G ́ Gomez et al. (2008)). We provide two characterizations of this new allocation rule. Following in Slikker's (2005a) footsteps, we characterize the probabilistic position value using probabilistic versions of component efficiency and balanced link con- tributions. Then we generalize the notion of link potential, defined by Slikker (2005b) for the class of deterministic communication situations, to the class of generalized probabilistic communication situations, and use it to characterize our allocation rule. Finally, we show that these two characterizations are logically equivalent.

Suggested Citation

  • Amandine Ghintran & Enrique Gonzalez-Aranguena & Conrado Manuel, 2011. "A probabilistic position value," Working Papers hal-00988137, HAL.
    • Handle: RePEc:hal:wpaper:hal-00988137
    Note: View the original document on HAL open archive server: https://hal.univ-lille.fr/hal-00988137
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    References listed on IDEAS

    as
    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. Hamiache, Gerard, 1999. "A Value with Incomplete Communication," Games and Economic Behavior, Elsevier, vol. 26(1), pages 59-78, January.
    3. 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.
    4. Xavier Chojnicki & Lionel Ragot, 2016. "Impacts of Immigration on an Ageing Welfare State: An Applied General Equilibrium Model for France," Fiscal Studies, Institute for Fiscal Studies, vol. 37, pages 258-284, June.
    5. K. Ortmann, 1998. "Conservation of energy in value theory," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 47(3), pages 423-449, October.
    6. Hart, Sergiu & Mas-Colell, Andreu, 1989. "Potential, Value, and Consistency," Econometrica, Econometric Society, vol. 57(3), pages 589-614, May.
    7. Roger B. Myerson, 1977. "Graphs and Cooperation in Games," Mathematics of Operations Research, INFORMS, vol. 2(3), pages 225-229, August.
    8. Daniel Gómez & Enrique Gonz{'a}lez-Arangüena & Conrado Manuel & Guillermo Owen & Monica Del Pozo, 2004. "A Unified Approach To The Myerson Value And The Position Value," Theory and Decision, Springer, vol. 56(2_2), pages 63-76, February.
    9. Sophie Dabo-Niang & Anne-Françoise Yao, 2013. "Kernel spatial density estimation in infinite dimension space," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 76(1), pages 19-52, January.
    10. Marco Slikker, 2005. "Link Monotonic Allocation Schemes," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 7(04), pages 473-489.
    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. William Thomson, 2001. "On the axiomatic method and its recent applications to game theory and resource allocation," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 18(2), pages 327-386.
    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:

    1. 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.
    2. 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.
    3. Sylvain Béal & André Casajus & Frank Huettner, 2018. "Efficient extensions of communication values," Annals of Operations Research, Springer, vol. 264(1), pages 41-56, May.
    4. Jilei Shi & Erfang Shan, 2021. "The Banzhaf value for generalized probabilistic communication situations," Annals of Operations Research, Springer, vol. 301(1), pages 225-244, June.
    5. Subhadip Chakrabarti & Loyimee Gogoi & Robert P. Gilles & Surajit Borkotokey & Rajnish Kumar, 2024. "Expected values for variable network games," Annals of Operations Research, Springer, vol. 336(3), pages 2061-2089, May.
    6. Julia Belau, 2012. "A New Outside Option Value for Networks: The Kappa-Value – Measuring Distribution of Power of Political Agreements," Ruhr Economic Papers 0326, Rheinisch-Westfälisches Institut für Wirtschaftsforschung, Ruhr-Universität Bochum, Universität Dortmund, Universität Duisburg-Essen.
    7. Jilei Shi & Lei Cai & Erfang Shan & Wenrong Lyu, 2022. "A value for cooperative games with coalition and probabilistic graph structures," Journal of Combinatorial Optimization, Springer, vol. 43(3), pages 646-671, April.
    8. Surajit Borkotokey & Sujata Gowala & Rajnish Kumar, 2023. "The Expected Shapley value on a class of probabilistic games," Papers 2308.03489, arXiv.org.
    9. Hayat, Muhammad Azmat & Farvaque, Etienne, 2012. "Public attitudes towards central bank independence: Lessons from the foundation of the ECB," European Journal of Political Economy, Elsevier, vol. 28(4), pages 512-523.
    10. 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.
    11. Borkotokey, Surajit & Chakrabarti, Subhadip & Gilles, Robert P. & Gogoi, Loyimee & Kumar, Rajnish, 2021. "Probabilistic network values," Mathematical Social Sciences, Elsevier, vol. 113(C), pages 169-180.
    12. van den Nouweland, Anne & Slikker, Marco, 2012. "An axiomatic characterization of the position value for network situations," Mathematical Social Sciences, Elsevier, vol. 64(3), pages 266-271.
    13. repec:zbw:rwirep:0326 is not listed on IDEAS
    14. repec:hal:pseose:halshs-01207823 is not listed on IDEAS
    15. Belau, Julia, 2012. "A New Outside Option Value for Networks: The Kappa-Value – Measuring Distribution of Power of Political Agreements," Ruhr Economic Papers 326, RWI - Leibniz-Institut für Wirtschaftsforschung, Ruhr-University Bochum, TU Dortmund University, University of Duisburg-Essen.

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