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Mathematical Methods of Operations Research

, Volume 66, Issue 2, pp 255–261 | Cite as

Owen coalitional value without additivity axiom

  • Anna B. Khmelnitskaya
  • Elena B. Yanovskaya
Original Article

Abstract

We show that the Owen value for TU games with coalition structure can be characterized without the additivity axiom similarly as it was done by Young for the Shapley value for general TU games. Our axiomatization via four axioms of efficiency, marginality, symmetry across coalitions, and symmetry within coalitions is obtained from the original Owen’s one by the replacement of additivity and null-player via marginality. We show that the alike axiomatization for the generalization of the Owen value suggested by Winter for games with level structure is valid as well.

Keywords

Cooperative TU game Coalitional structure Owen value Axiomatic characterization Marginality 

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References

  1. Kamijo Y (2005) Marginality in cooperative games with coalition structures. Unpublished manuscript, Graduate school of economics. Waseda university, Tokyo, JapanGoogle Scholar
  2. Khmelnitskaya AB (2003) Shapley value for constant-sum games. Int J Game Theory 32:223–227zbMATHCrossRefMathSciNetGoogle Scholar
  3. Owen G (1977) Values of games with a priori unions. In: Henn R, Moeschlin O (eds) Essays in mathematical economics and game theory. Springer, Berlin Heidelberg New York, pp 76–88Google Scholar
  4. Shapley LS (1953) A value for n-person games. In: Tucker AW, Kuhn HW (eds) Contributions to the theory of games II. Princeton University Press, Princeton, pp 307–317Google Scholar
  5. Vaźquez-Brage M (1998) Contribuciones a la teoriá del valor en juegos con utilidad transferible. PhD thesis. University of Santiago de Compostela, Spain (in Spanish)Google Scholar
  6. Winter E (1989) A value for games with level structures. Int J Game Theory 18:227–242zbMATHCrossRefMathSciNetGoogle Scholar
  7. Young HP (1985) Monotonic solutions of cooperative games. Int J Game Theory 14:65–72zbMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag 2007

Authors and Affiliations

  1. 1.SPb Institute for Economics and Mathematics Russian Academy of SciencesSt.PetersburgRussia

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