TY - JOUR
T1 - Cooperative Games on Antimatroids
AU - Algaba, E.
AU - Bilbao, J.M.
AU - van den Brink, J.R.
AU - Jimenez-Losada, A.
PY - 2004
Y1 - 2004
N2 - 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.
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
SP - 1
EP - 15
JO - Discrete Mathematics
JF - Discrete Mathematics
SN - 0012-365X
ER -