Cooperative Games on Antimatroids

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

doi:10.1016/j.disc.2003.10.019

Cooperative Games on Antimatroids

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

Research output: Contribution to Journal › Article › Academic › peer-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 language	English
Pages (from-to)	1-15
Number of pages	14
Journal	Discrete Mathematics
Volume	282
DOIs	https://doi.org/10.1016/j.disc.2003.10.019
Publication status	Published - 2004

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title = "Cooperative Games on Antimatroids",

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. {\textcopyright} 2004 Elsevier B.V. All rights reserved.",

author = "E. Algaba and J.M. Bilbao and {van den Brink}, J.R. and A. Jimenez-Losada",

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AU - Bilbao, J.M.

AU - van den Brink, J.R.

AU - Jimenez-Losada, A.

PY - 2004

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AB - 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.

U2 - 10.1016/j.disc.2003.10.019

DO - 10.1016/j.disc.2003.10.019

M3 - Article

VL - 282

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EP - 15

JO - Discrete Mathematics

JF - Discrete Mathematics

SN - 0012-365X

ER -