Abstract
Pure bargaining problems with transferable utility are considered. By associating a quasi-additive cooperative game with each one of them, a Shapley rule for this class of problems is derived from the Shapley value for games. The analysis of this new rule includes axiomatic characterizations and a comparison with the proportional rule.
This chapter has been published in Homo Oeconomicus 28(3), 2011.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Aadland, D., & Kolpin, V. (1998). Shared irrigation costs: An empirical and axiomatic analysis. Mathematical Social Sciences, 849, 203–218.
Bergantiños, G., & Vidal-Puga, J. J. (2007). The optimistic TU game in minimum cost spanning tree problems. International Journal of Game Theory, 36, 223–239.
van den Brink, R., & Funaki, Y. (2009). Axiomatizations of a class of equal surplus sharing solutions for TU-games. Theory and Decision, 67, 303–340.
Carreras, F., & Freixas, J. (2000). A note on regular semivalues. International Game Theory Review, 2, 345–352.
Driessen, T. S. H., & Funaki, Y. (1991). Coincidence of and collinearity between game theoretic solutions. OR Spektrum, 13, 15–30.
Gillies, D. B. (1953). Some theorems on n-person games. Ph.D. Thesis. Princeton University.
Hart, S., & Mas-Colell, A. (1988). The potential of the shapley value. In A. E. Roth (Ed.), The shapley value: essays in honor of Lloyd S. Shapley (pp. 127–137). Cambridge: Cambridge University Press.
Hart, S., & Mas-Colell, A. (1989). Potential, value and consistency. Econometrica, 57, 589–614.
Isbell, J. R. (1956). A class of majority games. Quarterly Journal of Mathematics, 7, 183–187.
Kalai, E., & Smorodinsky, M. (1975). Alternative solutions to Nash’s bargaining problem. Econometrica, 43, 513–518.
Kalai, E. (1977). Proportional solutions to bargaining situations: Interpersonal utility comparisons. Econometrica, 45, 1623–1630.
Megiddo, N. (1974). On the nonmonotonicity of the bargaining set, the kernel, and the nucleolus of a game. SIAM Journal of Applied Mathematics, 27, 355–358.
Nash, J. F. (1950). The bargaining problem. Econometrica, 18, 155–162.
von Neumann, J., & Morgenstern, O. (1944). Theory of games and economic behavior. Princeton: Princeton University Press.
Ortmann, K. M. (2000). The proportional value for positive cooperative games. Mathematical Methods of Operations Research, 51, 235–248.
Owen, G. (1995). Game theory. New York : Academic Press.
Roth, A. E. (Ed.). (1988). The shapley vlue: Essays in honor of Lloyd S. Shapley: Cambridge University Press.
Shapley, L. S. (1953). A value for \(n\)-person games. Annals of Mathematical Studies, 28, 307–317.
Shapley, L. S. (1971). Cores of convex games. International Journal of Game Theory, 1, 11–26.
Shubik, M. (1962). Incentives, decentralized control, the assignment of joint costs, and internal pricing. Management Science, 8, 325–343.
Young, H. P. (1985). Monotonic solutions of cooperative games. International Journal of Game Theory, 14, 65–72.
Acknowledgments
Research partially supported by Grants SGR 2009–01029 of the Catalonia Government (Generalitat de Catalunya), and MTM 2012–34426 of the Economy and Competitiveness Spanish Ministry.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Carreras, F., Owen, G. (2013). Pure Bargaining Problems and the Shapley Rule. In: Holler, M., Nurmi, H. (eds) Power, Voting, and Voting Power: 30 Years After. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-35929-3_36
Download citation
DOI: https://doi.org/10.1007/978-3-642-35929-3_36
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-35928-6
Online ISBN: 978-3-642-35929-3
eBook Packages: Business and EconomicsEconomics and Finance (R0)