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The Shapley value for games on matroids: The dynamic model

Author

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

Abstract

According to the work of Faigle [3] a static Shapley value for games on matroids has been introduced in Bilbao, Driessen, Jiménez-Losada and Lebrón [1]. In this paper we present a dynamic Shapley value by using a dynamic model which is based on a recursive sequence of static models. In this new model for games on matroids, our main result is that there exists a unique value satisfying analogous axioms to the classical Shapley value. Moreover, we obtain a recursive formula to calculate this dynamic Shapley value. Finally, we prove that its components are probabilistic values. Copyright Springer-Verlag Berlin Heidelberg 2002

Suggested Citation

  • J. M. Bilbao & T. S. H. Driessen & A. Jiménez-Losada & E. Lebrón, 2002. "The Shapley value for games on matroids: The dynamic model," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 56(2), pages 287-301, November.
    • Handle: RePEc:spr:mathme:v:56:y:2002:i:2:p:287-301
    DOI: 10.1007/s001860200213
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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.

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