TY - JOUR

T1 - 1-concave basis for TU games and the library game

AU - Driessen, T.S.H.

AU - Khmelnitskaya, A.B.

AU - Sales, Jordi

PY - 2012

Y1 - 2012

N2 - The study of 1-convex/1-concave TU games possessing a nonempty core and for which the nucleolus is linear was initiated by Driessen and Tijs (Methods Oper. Res. 46:395-406, 1983) and Driessen (OR Spectrum 7:19-26, 1985). However, until recently appealing abstract and practical examples of these classes of games were missing. The paper solves these drawbacks. We introduce a 1-concave basis for the entire space of all TU games wherefrom it follows that every TU game is either 1-convex/1-concave or is a sum of 1-convex and 1-concave games. Thus we may conclude that the classes of 1-convex/1-concave games constitute rather considerable subsets in the entire game space. On the other hand, an appealing practical example of 1-concave game has cropped up in Sales's study (Ph. D. thesis, 2002) of Catalan university library consortium for subscription to journals issued by Kluwer publishing house. The so-called library game turns out to be decomposable into suitably chosen 1-concave games of the basis mentioned above.

AB - The study of 1-convex/1-concave TU games possessing a nonempty core and for which the nucleolus is linear was initiated by Driessen and Tijs (Methods Oper. Res. 46:395-406, 1983) and Driessen (OR Spectrum 7:19-26, 1985). However, until recently appealing abstract and practical examples of these classes of games were missing. The paper solves these drawbacks. We introduce a 1-concave basis for the entire space of all TU games wherefrom it follows that every TU game is either 1-convex/1-concave or is a sum of 1-convex and 1-concave games. Thus we may conclude that the classes of 1-convex/1-concave games constitute rather considerable subsets in the entire game space. On the other hand, an appealing practical example of 1-concave game has cropped up in Sales's study (Ph. D. thesis, 2002) of Catalan university library consortium for subscription to journals issued by Kluwer publishing house. The so-called library game turns out to be decomposable into suitably chosen 1-concave games of the basis mentioned above.

KW - Cooperative TU game 1-concavity Library cost game Shapley value Nucleolus

U2 - DOI: 10.1007/s11750-010-0157-5

DO - DOI: 10.1007/s11750-010-0157-5

M3 - Article

VL - 20

SP - 578

EP - 591

JO - Trabajos de Investigacion Operativa

JF - Trabajos de Investigacion Operativa

SN - 0213-8204

IS - 3

ER -