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|
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- Chun, Youngsub, 1988. "The equal-loss principle for bargaining problems," Economics Letters, Elsevier, vol. 26(2), pages 103-106.
- Herrero, Carmen & Marco, Maria Carmen, 1993. "Rational equal-loss solutions for bargaining problems," Mathematical Social Sciences, Elsevier, vol. 26(3), pages 273-286, November.
- Sunil Gupta, 1989. "Modeling Integrative, Multiple Issue Bargaining," Management Science, INFORMS, vol. 35(7), pages 788-806, July.
- Kalai, Ehud, 1977.
"Proportional Solutions to Bargaining Situations: Interpersonal Utility Comparisons,"
Econometric Society, vol. 45(7), pages 1623-1630, October.
- Ehud Kalai, 1977. "Proportional Solutions to Bargaining Situations: Interpersonal Utility Comparisons," Discussion Papers 179, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
- Nash, John, 1950. "The Bargaining Problem," Econometrica, Econometric Society, vol. 18(2), pages 155-162, April.
- Nejat Anbarci, 1995. "Reference Functions and Balanced Concessions in Bargaining," Canadian Journal of Economics, Canadian Economics Association, vol. 28(3), pages 675-682, August.
- Dubra, Juan, 2001. "An asymmetric Kalai-Smorodinsky solution," Economics Letters, Elsevier, vol. 73(2), pages 131-136, November.
- 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 Elsevier.
- Robert W. Rosenthal, 1976. "An Arbitration Model for Normal-Form Games," Mathematics of Operations Research, INFORMS, vol. 1(1), pages 82-88, February.
- 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.
- 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.
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