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

  • Jun Su
  • Theo S. H. Driessen
  • Gen-Jiu XuEmail author


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.


Cooperative game Reduced game Shapley value Linear value Sobolev’s consistency 

Mathematics Subject Classification

91A06 91A12 


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Copyright information

© Operations Research Society of China, Periodicals Agency of Shanghai University, Science Press, and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.School of ScienceXi’an University of Science and TechnologyXi’anChina
  2. 2.Department of Applied MathematicsUniversity of TwenteEnschedeThe Netherlands
  3. 3.Department of Applied MathematicsNorthwestern Polytechnical UniversityXi’anChina

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