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1-concave basis for TU games and the library game

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  • Theo Driessen
  • Anna Khmelnitskaya
  • Jordi Sales

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

Suggested Citation

  • Theo Driessen & Anna Khmelnitskaya & Jordi Sales, 2012. "1-concave basis for TU games and the library game," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 20(3), pages 578-591, October.
    • Handle: RePEc:spr:topjnl:v:20:y:2012:i:3:p:578-591
    DOI: 10.1007/s11750-010-0157-5
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    References listed on IDEAS

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    1. SCHMEIDLER, David, 1969. "The nucleolus of a characteristic function game," LIDAM Reprints CORE 44, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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    Cited by:

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    2. Satoshi Masuya & Masahiro Inuiguchi, 2016. "A fundamental study for partially defined cooperative games," Fuzzy Optimization and Decision Making, Springer, vol. 15(3), pages 281-306, September.

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