Abstract.
Cooperative games on antimatroids are cooperative games restricted by a combinatorial structure which generalize the permission structure. So, cooperative games on antimatroids group several well-known families of games which have important applications in economics and politics. Therefore, the study of the rectricted games by antimatroids allows to unify criteria of various lines of research. The current paper establishes axioms that determine the restricted Shapley value on antimatroids by conditions on the cooperative game v and the structure determined by the antimatroid. This axiomatization generalizes the axiomatizations of both the conjunctive and disjunctive permission value for games with a permission structure. We also provide an axiomatization of the Shapley value restricted to the smaller class of poset antimatroids. Finally, we apply our model to auction situations.
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Manuscript received: May 2002/Final version received: September 2002
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ID="*" This research has been partially supported by the Spanish Ministery of Science and Technology, under grant SEC2000–1243. Financial support by the Netherlands Organization for Scientific Research (NWO), ESR-grant 510-01-0504 is gratefully acknowledged.
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Algaba, E., Bilbao, J., van den Brink, R. et al. Axiomatizations of the Shapley value for cooperative games on antimatroids. Mathematical Methods of OR 57, 49–65 (2003). https://doi.org/10.1007/s001860200250
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DOI: https://doi.org/10.1007/s001860200250