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Values of games with weighted graphs

Author

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  • González–Arangüena, Enrique
  • Manuel, Conrado Miguel
  • del Pozo, Mónica

Abstract

In this paper we deal with TU games in which cooperation is restricted by means of a weighted network. We admit several interpretations for the weight of a link: capacity of the communication channel, flow across it, intimacy or intensity in the relation, distance between both incident nodes/players, cost of building or maintaining the communication link or even probability of the relation (as in Calvo, Lasaga, and van den Noweland, 1999). Then, according to the different interpretations, we introduce several point solutions for these restricted games in a way parallel to the familiar environment of Myerson. Finally, we characterize these values in terms of the (adapted) component efficiency, fairness and balanced contributions properties and we analyze the extent to which they satisfy a link/weight monotonicity property.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:ejores:v:243:y:2015:i:1:p:248-257
    DOI: 10.1016/j.ejor.2014.11.033
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    References listed on IDEAS

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    1. Lindelauf, R.H.A. & Hamers, H.J.M. & Husslage, B.G.M., 2013. "Cooperative game theoretic centrality analysis of terrorist networks: The cases of Jemaah Islamiyah and Al Qaeda," European Journal of Operational Research, Elsevier, vol. 229(1), pages 230-238.
    2. Roger B. Myerson, 1977. "Graphs and Cooperation in Games," Mathematics of Operations Research, INFORMS, vol. 2(3), pages 225-229, August.
    3. Jiménez-Losada, Andrés & Fernández, Julio R. & Ordóñez, Manuel & Grabisch, Michel, 2010. "Games on fuzzy communication structures with Choquet players," European Journal of Operational Research, Elsevier, vol. 207(2), pages 836-847, December.
    4. 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.
    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.
    6. 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(1), pages 63-76, April.
    7. 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. Sylvain Béal & Eric Rémila & Philippe Solal, 2015. "Discounted Tree Solutions," Working Papers hal-01377923, HAL.
    2. 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.
    3. 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.
    4. Taiki Yamada, 2021. "New allocation rule of directed hypergraphs," Papers 2110.06506, arXiv.org, revised Feb 2023.

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