Fairness, Efficiency, and the Nash Bargaining Solution
A bargaining solution balances fairness and efficiency if each player's payoff lies between the minimum and maximum of the payoffs assigned to him by the egalitarian and utilitarian solutions. In the 2-person bargaining problem, the Nash solution is the unique scale-invariant solution satisfying this property. Additionally, a similar result, relating the weighted egalitarian and utilitarian solutions to a weighted Nash solution, is obtained. These results are related to a theorem of Shapley, which I generalize. For n>=3, there does not exist any n-person scale-invariant bargaining solution that balances fairness and efficiency.
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- Samet, Dov & Safra, Zvi, 2005. "A family of ordinal solutions to bargaining problems with many players," Games and Economic Behavior, Elsevier, vol. 50(1), pages 89-106, January.
- Nejat Anbarci, 1998. "Simple Characterizations of the Nash and Kalai/smorodinsky Solutions," Theory and Decision, Springer, vol. 45(3), pages 255-261, December.
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