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.
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Manuscript received: August 2001/Final version received: February 2002
Acknowledgements. We would like to express our gratitude to an anonymous referee for interesting comments and for their careful reading of the manuscript.
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Bilbao, J., Driessen, T., Jiménez-Losada, A. et al. The Shapley value for games on matroids: The dynamic model. Mathematical Methods of OR 56, 287–301 (2002). https://doi.org/10.1007/s001860200213
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DOI: https://doi.org/10.1007/s001860200213