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The Shapley value for games on matroids: The static model

Author

Listed:
  • J. M. Bilbao
  • T. S. H. Driessen
  • A. Jiménez Losada
  • E. Lebrón

Abstract

In the classical model of cooperative games, it is considered that each coalition of players can form and cooperate to obtain its worth. However, we can think that in some situations this assumption is not real, that is, all the coalitions are not feasible. This suggests that it is necessary to rise the whole question of generalizing the concept of cooperative game, and therefore to introduce appropriate solution concepts. We propose a model for games on a matroid, based in several important properties of this combinatorial structure and we introduce the probabilistic Shapley value for games on matroids. Copyright Springer-Verlag Berlin Heidelberg 2001

Suggested Citation

  • J. M. Bilbao & T. S. H. Driessen & A. Jiménez Losada & E. Lebrón, 2001. "The Shapley value for games on matroids: The static model," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 53(2), pages 333-348, June.
    • Handle: RePEc:spr:mathme:v:53:y:2001:i:2:p:333-348
    DOI: 10.1007/s001860100111
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    Citations

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    Cited by:

    1. Meng, Fanyong & Chen, Xiaohong & Zhang, Qiang, 2015. "A coalitional value for games on convex geometries with a coalition structure," Applied Mathematics and Computation, Elsevier, vol. 266(C), pages 605-614.
    2. Emilio Calvo & Esther Gutiérrez-López, 2015. "The value in games with restricted cooperation," Discussion Papers in Economic Behaviour 0115, University of Valencia, ERI-CES.
    3. Zhengxing Zou & Qiang Zhang & Surajit Borkotokey & Xiaohui Yu, 2020. "The extended Shapley value for generalized cooperative games under precedence constraints," Operational Research, Springer, vol. 20(2), pages 899-925, June.

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