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.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
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, Princeton
Kalai E, Samet D (1985) Monotonic solutions to general cooperative games. Econometrica 53/2: 307–327
Maschler M (1982) The worth of a cooperative enterprise to each member. In: Games, economic dynamics and time series analysis
Owen G (1968) A note on the Shapley value. Management Science 14/11:731–732
Owen G (1972) Multilinear extensions of games. Management Science 18/5:P64-P79
Owen G (1982) Game theory, 2nd ed. Academic Press, New York
Shapley LS (1953a) Additive and non-additive set functions. PhD Thesis, Department of Mathematics, Princeton University
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, Princeton
Shapley LS (1982) Discussant's comment. In: Moriarity S (ed) Joint cost allocation. University of Oklahoma Press, Tulsa
Author information
Authors and Affiliations
Additional information
Financial support for this research was granted by the National Science Foundation's Economics Division, Grant No. SOC-7907542.
Rights and permissions
About this article
Cite this article
Kalai, E., Samet, D. On weighted Shapley values. Int J Game Theory 16, 205–222 (1987). https://doi.org/10.1007/BF01756292
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01756292