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1-concave basis for TU games and the library game
Driessen, T.S.H. and Khmelnitskaya, A.B. and Sales, J. (2012) 1-concave basis for TU games and the library game. Top, 20 (3). pp. 578-591. ISSN 1134-5764
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| Abstract: | 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. |
| Item Type: | Article |
| Copyright: | © 2012 Springer |
| Faculty: | Electrical Engineering, Mathematics and Computer Science (EEMCS) |
| Research Group: | |
| Link to this item: | http://purl.utwente.nl/publications/82130 |
| Official URL: | http://dx.doi.org/10.1007/s11750-010-0157-5 |
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