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Weighted Proportional Losses Solution

Author

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  • Jaume García Segarra

    () (Fundamentos del Análisis Económico (Economics Department), Universitat Jaume I)

  • Miguel Ginés Vilar

    () (Fundamentos del Análisis Económico (Economics Department), Universitat Jaume I)

Abstract

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.

Suggested Citation

  • Jaume García Segarra & Miguel Ginés Vilar, 2011. "Weighted Proportional Losses Solution," ThE Papers 10/21, Department of Economic Theory and Economic History of the University of Granada..
  • Handle: RePEc:gra:wpaper:10/21
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    References listed on IDEAS

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    9. 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.
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    11. Chun, Youngsub, 1988. "The equal-loss principle for bargaining problems," Economics Letters, Elsevier, vol. 26(2), pages 103-106.
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