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A probabilistic position value

Author

Listed:
  • A. Ghintran

    ()

  • E. González-Arangüena

    ()

  • C. Manuel

    ()

Abstract

In this article, we generalize the position value, defined by Meessen (Master’s thesis, 1988 ) for the class of deterministic communication situations, to the class of generalized probabilistic communication situations (Gómez et al. in European Journal of Operational Research 190:539–556, 2008 ). We provide two characterizations of this new allocation rule. Following in Slikker’s (International Journal of Game Theory 33:505–514, 2005a ) footsteps, we characterize the probabilistic position value using probabilistic versions of component efficiency and balanced link contributions. Then we generalize the notion of link potential, defined by Slikker (International Game Theory Review 7:473–489, 2005b ) for the class of deterministic communication situations, to the class of generalized probabilistic communication situations, and use it to characterize our allocation rule. Copyright Springer Science+Business Media, LLC 2012

Suggested Citation

  • A. Ghintran & E. González-Arangüena & C. Manuel, 2012. "A probabilistic position value," Annals of Operations Research, Springer, vol. 201(1), pages 183-196, December.
  • Handle: RePEc:spr:annopr:v:201:y:2012:i:1:p:183-196:10.1007/s10479-012-1195-1
    DOI: 10.1007/s10479-012-1195-1
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    References listed on IDEAS

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    1. Hamiache, Gerard, 1999. "A Value with Incomplete Communication," Games and Economic Behavior, Elsevier, vol. 26(1), pages 59-78, January.
    2. Xavier Chojnicki & Lionel Ragot, 2011. "Impacts of Immigration on Aging Welfare-State An Applied General Equilibrium Model for France," Working Papers 2011-13, CEPII research center.
    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. Hart, Sergiu & Mas-Colell, Andreu, 1989. "Potential, Value, and Consistency," Econometrica, Econometric Society, vol. 57(3), pages 589-614, May.
    5. repec:spr:compst:v:47:y:1998:i:3:p:423-449 is not listed on IDEAS
    6. 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.
    7. 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.
    8. 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.
    9. 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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    Citations

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    Cited by:

    1. Jean-François Caulier & Michel Grabisch & Agnieszka Rusinowska, 2013. "An allocation rule for dynamic random network formation processes," Post-Print halshs-00881125, HAL.
    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. repec:spr:annopr:v:264:y:2018:i:1:d:10.1007_s10479-017-2661-6 is not listed on IDEAS
    4. repec:zbw:rwirep:0326 is not listed on IDEAS
    5. Jean-François Caulier & Michel Grabisch & Agnieszka Rusinowska, 2015. "An allocation rule for dynamic random network formation," PSE - Labex "OSE-Ouvrir la Science Economique" halshs-01207823, HAL.
    6. Sylvain Béal & André Casajus & Frank Huettner, 2018. "Efficient extensions of communication values," Annals of Operations Research, Springer, vol. 264(1), pages 41-56, May.
    7. 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.
    8. repec:spr:sochwe:v:50:y:2018:i:1:d:10.1007_s00355-017-1074-4 is not listed on IDEAS
    9. 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.
    10. 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.
    11. Jean-François Caulier & Michel Grabisch & Agnieszka Rusinowska, 2015. "An allocation rule for dynamic random network formation," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-01207823, HAL.
    12. 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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