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Cooperation among agents with a proximity relation

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  • Fernández, J.R.
  • Gallego, I.
  • Jiménez-Losada, A.
  • Ordóñez, M.

Abstract

A cooperative game consists of a set of players and a characteristic function determining the maximal gain or minimal cost that every subset of players can achieve when they decide to cooperate, regardless of the actions that the other players take. The relationships of closeness among the players should modify the bargaining among them and therefore their payoffs. The first models that have studied this closeness used a priori unions or undirected graphs. In the a priori union model a partition of the big coalition is supposed. Each element of the partition represents a group of players with the same interests. The groups negotiate among them to form the grand coalition and later, inside each one, players bargain among them. Now we propose to use proximity relations to represent leveled closeness of the interests among the players and extending the a priori unions model.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:ejores:v:250:y:2016:i:2:p:555-565
    DOI: 10.1016/j.ejor.2015.09.029
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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.
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    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. AUMANN, Robert J. & DREZE, Jacques H., 1974. "Cooperative games with coalition structures," LIDAM Reprints CORE 217, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    5. De Waegenaere, Anja & Wakker, Peter P., 2001. "Nonmonotonic Choquet integrals," Journal of Mathematical Economics, Elsevier, vol. 36(1), pages 45-60, September.
    6. 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. M. G. Fiestras-Janeiro & I. García-Jurado & A. Meca & M. A. Mosquera, 2020. "On benefits of cooperation under strategic power," Annals of Operations Research, Springer, vol. 288(1), pages 285-306, May.
    2. Stefani, Silvana & Ausloos, Marcel & González-Concepción, Concepción & Sonubi, Adeyemi & Gil-Fariña, Ma Candelaria & Pestano-Gabino, Celina & Moretto, Enrico, 2021. "Competing or collaborating, with no symmetrical behaviour: Leadership opportunities and winning strategies under stability," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 187(C), pages 489-504.

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