1-concave basis for TU games and the library game

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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)
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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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