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Games on fuzzy communication structures with Choquet players

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  • Jiménez-Losada, Andrés
  • Fernández, Julio R.
  • Ordóñez, Manuel
  • Grabisch, Michel

Abstract

Myerson (1977) used graph-theoretic ideas to analyze cooperation structures in games. In his model, he considered the players in a cooperative game as vertices of a graph, which undirected edges defined their communication possibilities. He modified the initial games taking into account the graph and he established a fair allocation rule based on applying the Shapley value to the modified game. Now, we consider a fuzzy graph to introduce leveled communications. In this paper players play in a particular cooperative way: they are always interested first in the biggest feasible coalition and second in the greatest level (Choquet players). We propose a modified game for this situation and a rule of the Myerson kind.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:ejores:v:207:y:2010:i:2:p:836-847
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    References listed on IDEAS

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    1. Tsurumi, Masayo & Tanino, Tetsuzo & Inuiguchi, Masahiro, 2001. "A Shapley function on a class of cooperative fuzzy games," European Journal of Operational Research, Elsevier, vol. 129(3), pages 596-618, March.
    2. Jean-Pierre Aubin, 1981. "Cooperative Fuzzy Games," Mathematics of Operations Research, INFORMS, vol. 6(1), pages 1-13, February.
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    Cited by:

    1. Conrado M. Manuel & Daniel Martín, 2020. "A Monotonic Weighted Shapley Value," Group Decision and Negotiation, Springer, vol. 29(4), pages 627-654, August.
    2. Conrado M. Manuel & Daniel Martín, 2021. "A Monotonic Weighted Banzhaf Value for Voting Games," Mathematics, MDPI, vol. 9(12), pages 1-23, June.
    3. 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.
    4. Li, Deng-Feng, 2012. "A fast approach to compute fuzzy values of matrix games with payoffs of triangular fuzzy numbers," European Journal of Operational Research, Elsevier, vol. 223(2), pages 421-429.
    5. René Brink, 2017. "Games with a permission structure - A survey on generalizations and applications," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 25(1), pages 1-33, April.
    6. 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.
    7. J. R. Fernández & I. Gallego & A. Jiménez-Losada & M. Ordóñez, 2019. "The cg-average tree value for games on cycle-free fuzzy communication structures," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 27(3), pages 456-478, October.
    8. Fernández, J.R. & Gallego, I. & Jiménez-Losada, A. & Ordóñez, M., 2016. "Cooperation among agents with a proximity relation," European Journal of Operational Research, Elsevier, vol. 250(2), pages 555-565.
    9. Sanjiv Kumar & Ritika Chopra & Ratnesh R. Saxena, 2016. "A Fast Approach to Solve Matrix Games with Payoffs of Trapezoidal Fuzzy Numbers," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 33(06), pages 1-14, December.
    10. Jiacai Liu & Wenjian Zhao, 2016. "Cost-Sharing of Ecological Construction Based on Trapezoidal Intuitionistic Fuzzy Cooperative Games," IJERPH, MDPI, vol. 13(11), pages 1-12, November.

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