1-concave basis for TU games and the library game

Theo S.H. Driessen, Anna B. Khmelnitskaya*, Jordi Sales

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

7 Citations (Scopus)

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.
Original languageEnglish
Pages (from-to)578-591
Number of pages14
JournalTop
Volume20
Issue number3
DOIs
Publication statusPublished - 2012

Keywords

  • MSC-91A12
  • Cooperative TU game
  • 1-concavity
  • Library cost game
  • Shapleyvalue
  • Nucleolus

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