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International Journal of Game Theory

, Volume 16, Issue 3, pp 205–222 | Cite as

On weighted Shapley values

  • E. Kalai
  • D. Samet
Article

Abstract

Nonsymmetric Shapley values for coalitional form games with transferable utility are studied. The nonsymmetries are modeled through nonsymmetric weight systems defined on the players of the games. It is shown axiomatically that two families of solutions of this type are possible. These families are strongly related to each other through the duality relationship on games. While the first family lends itself to applications of nonsymmetric revenue sharing problems the second family is suitable for applications of cost allocation problems. The intersection of these two families consists essentially of the symmetric Shapley value. These families are also characterized by a probabilistic arrival time to the game approach. It is also demonstrated that lack of symmetries may arise naturally when players in a game represent nonequal size constituencies.

Keywords

Arrival Time Economic Theory Game Theory Allocation Problem Coalitional Form 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. Harsanyi JC.(1959) A bargaining model for cooperativen-person games. In: Tucker AW, Luce RD (eds) Contributions to the theory of games IV (Annals of Mathematics Studies 40, pp 325–355). Princeton University Press, PrincetonGoogle Scholar
  2. Kalai E, Samet D (1985) Monotonic solutions to general cooperative games. Econometrica 53/2: 307–327Google Scholar
  3. Maschler M (1982) The worth of a cooperative enterprise to each member. In: Games, economic dynamics and time series analysisGoogle Scholar
  4. Owen G (1968) A note on the Shapley value. Management Science 14/11:731–732Google Scholar
  5. Owen G (1972) Multilinear extensions of games. Management Science 18/5:P64-P79Google Scholar
  6. Owen G (1982) Game theory, 2nd ed. Academic Press, New YorkGoogle Scholar
  7. Shapley LS (1953a) Additive and non-additive set functions. PhD Thesis, Department of Mathematics, Princeton UniversityGoogle Scholar
  8. Shapley LS (1953b) A value forn-person games. In: Kuhn HW, Tucker AW (eds) Contributions to the theory of games II (Annals of Mathematics Studies 28, pp 307–317). Princeton University Press, PrincetonGoogle Scholar
  9. Shapley LS (1982) Discussant's comment. In: Moriarity S (ed) Joint cost allocation. University of Oklahoma Press, TulsaGoogle Scholar

Copyright information

© Physica-Verlag 1987

Authors and Affiliations

  • E. Kalai
    • 1
  • D. Samet
    • 2
  1. 1.Department of Managerial Economics and Decision Sciences, J. L. Kellogg Graduate School of ManagementNorthwestern UniversityEvanstonUSA
  2. 2.Department of EconomicsBar-Ilan UniversityRamat-GanIsrael

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