Cooperative Games on Antimatroids

E. Algaba, J.M. Bilbao, J.R. van den Brink, A. Jimenez-Losada

    Research output: Contribution to JournalArticleAcademicpeer-review

    Abstract

    The aim of this paper is to introduce cooperative games with a feasible coalition system which is called antimatroid. These combinatorial structures generalize the permission structures, which have nice economical applications. With this goal, we first characterize the approaches from a permission structure with special classes of antimatroids. Next, we use the concept of interior operator in an antimatroid and we define the restricted game taking into account the limited possibilities of cooperation determined by the antimatroid. These games extend the restricted games obtained by permission structures. Finally, we provide a computational method to obtain the Shapley and Banzhaf values of the players in the restricted game, by using the worths of the original game. © 2004 Elsevier B.V. All rights reserved.
    Original languageEnglish
    Pages (from-to)1-15
    Number of pages14
    JournalDiscrete Mathematics
    Volume282
    DOIs
    Publication statusPublished - 2004

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