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A value for generalized probabilistic communication situations

Author

Listed:
  • Gómez, D.
  • González-Arangüena, E.
  • Manuel, C.
  • Owen, G.

Abstract

We introduce in this work an extension of the model of games with probabilistic graphs arising in Calvo et al. (1999, Math. Soc. Sci. 37, 79), which itself generalizes the one developed by Myerson (1977, Math. of Oper. Res. 2, 225) for games with communications restrictions. In the first of these models, each pair of nodes has a given probability of direct communication. In this paper a more general setting is considered: we suppose that a probability distribution over the set of all possible communication networks among the players is given. A generalization of the Myerson value is defined and characterized in this context.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:ejores:v:190:y:2008:i:2:p:539-556
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    References listed on IDEAS

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    1. Jackson, Matthew O., 2005. "Allocation rules for network games," Games and Economic Behavior, Elsevier, vol. 51(1), pages 128-154, April.
    2. Roger B. Myerson, 1977. "Graphs and Cooperation in Games," Mathematics of Operations Research, INFORMS, vol. 2(3), pages 225-229, August.
    3. 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.
    4. van den Nouweland, Anne & Borm, Peter, 1991. "On the Convexity of Communication Games," International Journal of Game Theory, Springer;Game Theory Society, vol. 19(4), pages 421-430.
    5. 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.
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    Cited by:

    1. Subhadip Chakrabarti & Loyimee Gogoi & Robert P Gilles & Surajit Borkotokey & Rajnish Kumar, 2021. "Expected Values for Variable Network Games," Papers 2108.07047, arXiv.org, revised Oct 2022.
    2. A. Ghintran & E. González-Arangüena & C. Manuel, 2012. "A probabilistic position value," Annals of Operations Research, Springer, vol. 201(1), pages 183-196, December.
    3. Julia Belau, 2011. "Outside Options in Probabilistic Coalition Situations," Ruhr Economic Papers 0236, Rheinisch-Westfälisches Institut für Wirtschaftsforschung, Ruhr-Universität Bochum, Universität Dortmund, Universität Duisburg-Essen.
    4. Enrique González-Arangüena & Conrado Manuel & Daniel Gomez & René van den Brink, 2008. "A Value for Directed Communication Situations," Tinbergen Institute Discussion Papers 08-006/1, Tinbergen Institute.
    5. Gómez, Daniel & Figueira, José Rui & Eusébio, Augusto, 2013. "Modeling centrality measures in social network analysis using bi-criteria network flow optimization problems," European Journal of Operational Research, Elsevier, vol. 226(2), pages 354-365.
    6. 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.
    7. van den Brink, René & González-Arangüena, Enrique & Manuel, Conrado & del Pozo, Mónica, 2014. "Order monotonic solutions for generalized characteristic functions," European Journal of Operational Research, Elsevier, vol. 238(3), pages 786-796.
    8. 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.
    9. Julia Belau, 2011. "Outside Options In Probabilistic Coalition Situations," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 13(04), pages 417-442.
    10. 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.
    11. 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.
    12. repec:zbw:rwirep:0326 is not listed on IDEAS
    13. C. Manuel & D. Martín, 2021. "A value for communication situations with players having different bargaining abilities," Annals of Operations Research, Springer, vol. 301(1), pages 161-182, June.
    14. 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.
    15. repec:zbw:rwirep:0236 is not listed on IDEAS
    16. 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.
    17. Surajit Borkotokey & Sujata Gowala & Rajnish Kumar, 2023. "The Expected Shapley value on a class of probabilistic games," Papers 2308.03489, arXiv.org.
    18. 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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