1-concave basis for TU games and the library game

• Theo S.H. Driessen ^[1] ; Anna B. Khmelnitskaya ^[2] ; Jordi Sales ^[3]
  1. [1] University of Twente

     University of Twente

     Países Bajos

     
  2. [2] Russian Academy of Sciences

     Russian Academy of Sciences

     Rusia

     
  3. [3] Universitat de Barcelona

     Universitat de Barcelona

     Barcelona, España

     

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• Localización: Top, ISSN-e 1863-8279, ISSN 1134-5764, Vol. 20, Nº. 3, 2012, págs. 578-591
• Idioma: inglés
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• Resumen

  • 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.