1-concave basis for TU games and the library game

Theo Driessen (), Anna Khmelnitskaya () and Jordi Sales ()

TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, 2012, vol. 20, issue 3, 578-591

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. Copyright Sociedad de Estadística e Investigación Operativa 2012

Keywords: Cooperative TU game; 1-concavity; Library cost game; Shapley value; Nucleolus; 91A12; 91A40; 91A43 (search for similar items in EconPapers)
Date: 2012
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Citations: View citations in EconPapers (4)

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DOI: 10.1007/s11750-010-0157-5

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