Weighted Proportional Losses Solution
We propose and characterize a new solution for problems with asymmetric bargaining power among the agents that we named weighted proportional losses solution. It is specially interesting when agents are bargaining under restricted probabilistic uncertainty. The weighted proportional losses assigns to each agent losses proportional to her ideal utility and also proportional to her bargaining power. This solution is always individually rational, even for 3 or more agents and it can be seen as the normalized weighted equal losses solution. When bargaining power among the agents is equal, the weighted proportional losses solution becomes the Kalai-Smorodinsky solution. We characterize our solution in the basis of restricted monotonicity and restricted concavity. A consequence of this result is an alternative characterization of Kalai-Smorodinsky solution which includes contexts with some kind of uncertainty. Finally we show that weighted proportional losses solution satisfyies desirable properties as are strong Pareto optimality for 2 agents and continuity also fulfilled by Kalai-Smorodinsky solution, that are not satisfied either by weighted or asymmetric Kalai-Smorodinsky solutions.
|Date of creation:||01 Aug 2011|
|Date of revision:|
|Contact details of provider:|| Postal: Campus Universitario de Cartuja|
Web page: http://www.ugr.es/local/teoriahe
More information through EDIRC
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Herrero, Carmen & Marco, Maria Carmen, 1993. "Rational equal-loss solutions for bargaining problems," Mathematical Social Sciences, Elsevier, vol. 26(3), pages 273-286, November.
- Nash, John, 1950. "The Bargaining Problem," Econometrica, Econometric Society, vol. 18(2), pages 155-162, April.
- Dubra, J.M., 1998.
"An Asymmetric Kalai-Smorodinsky Solution,"
98-09, C.V. Starr Center for Applied Economics, New York University.
- Robert W. Rosenthal, 1975. "An Arbitration Model for Normal-Form Games," Discussion Papers 121, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
- Ehud Kalai, 1977.
"Proportional Solutions to Bargaining Situations: Interpersonal Utility Comparisons,"
179, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
- Kalai, Ehud, 1977. "Proportional Solutions to Bargaining Situations: Interpersonal Utility Comparisons," Econometrica, Econometric Society, vol. 45(7), pages 1623-30, October.
- Thomson, William, 1994.
"Cooperative models of bargaining,"
Handbook of Game Theory with Economic Applications,
in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 2, chapter 35, pages 1237-1284
- Anbarci, Nejat & Bigelow, John P., 1994. "The area monotonic solution to the cooperative bargaining problem," Mathematical Social Sciences, Elsevier, vol. 28(2), pages 133-142, October.
- Thomson, William, 1981. "A class of solutions to bargaining problems," Journal of Economic Theory, Elsevier, vol. 25(3), pages 431-441, December.
- Peters, H.J.M. & Tijs, S.H., 1985. "Characterization of all individually monotonic bargaining solutions," Other publications TiSEM 52f5a6d5-dcac-4fec-9b8e-9, Tilburg University, School of Economics and Management.
- Nejat Anbarci, 1995. "Reference Functions and Balanced Concessions in Bargaining," Canadian Journal of Economics, Canadian Economics Association, vol. 28(3), pages 675-82, August.
- Chun, Youngsub, 1988. "The equal-loss principle for bargaining problems," Economics Letters, Elsevier, vol. 26(2), pages 103-106.
- Sunil Gupta, 1989. "Modeling Integrative, Multiple Issue Bargaining," Management Science, INFORMS, vol. 35(7), pages 788-806, July.
When requesting a correction, please mention this item's handle: RePEc:gra:wpaper:10/21. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Angel Solano Garcia.)
If references are entirely missing, you can add them using this form.