Journal of the Operations Research Society of China ›› 2021, Vol. 9 ›› Issue (2): 344-357.doi: 10.1007/s40305-019-00279-4

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Generalizations of Sobolev’s Consistency and Values for TU-Games

Jun Su1, Theo S. H. Driessen2, Gen-Jiu Xu3   

  1. 1. School of Science, Xi'an University of Science and Technology, Xi'an 710054, China;
    2. Department of Applied Mathematics, University of Twente, 7500 AE Enschede, The Netherlands;
    3. Department of Applied Mathematics, Northwestern Polytechnical University, Xi'an 710072, China
  • Received:2018-07-06 Revised:2019-08-07 Online:2021-06-30 Published:2021-06-08
  • Contact: Gen-Jiu Xu, Jun Su, Theo S. H. Driessen E-mail:xugenjiu@nwpu.edu.cn;junsu99@126.com;t.s.h.driessen@ewi.utwente.nl
  • Supported by:
    This work was supported by the National Natural Science Foundation of China (Nos.11402194,71671140 and 71271171).

Abstract: In the framework of cooperative game theory, Sobolev (Advances in game theory, Izdat., “Minitis”, Vilnius, pp 151–153, 1973) axiomatized the well-known Shapley value by means of consistency property with reference to a specifically chosen reduced game. The goal of this paper is to generalize Sobolev’s consistency approach to the class of efficient, symmetric and linear values.

Key words: Cooperative game, Reduced game, Shapley value, Linear value, Sobolev’s consistency

CLC Number: