1-concave basis for TU games and the library game
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.
KeywordsCooperative TU game 1-concavity Library cost game Shapley value Nucleolus
Mathematics Subject Classification (2000)91A12 91A40 91A43
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- Driessen TSH, Tijs SH (1983) The τ-value, the nucleolus and the core for a subclass of games. Methods Oper Res 46:395–406 Google Scholar
- Sales J (2002) Models cooperatius d’assignació de costos en un consorci de biblioteques. PhD thesis, University of Barcelona, Spain, (in Catalan) Google Scholar
- Shapley LS (1953) A value for n-person games. In: Tucker AW, Kuhn HW (eds) Contributions to the theory of games. Princeton University Press, Princeton, pp 307–317 Google Scholar
- Tijs SH (1981) Bounds for the core and the τ-value. In: Moeschlin O, Pallaschke D (eds) Game theory and mathematical economics. North-Holland, Amsterdam, pp 123–132 Google Scholar