The Number of Outcomes in the Pareto-Optimal Set of Discrete Bargaining Games
A set of n players is to bargain over which one of m possible outcomes will be chosen. The preference of outcome i to player j is assumed to be a random variable with all preference rankings equally likely and without ties. This would arise in case the payoffs are chosen as independent samplings fro...
| Veröffentlicht in: | Mathematics of Operations Research. - Institute for Operations Research and the Management Sciences. - 6(1981), 4, Seite 571-578 |
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| 1. Verfasser: | |
| Format: | Online-Aufsatz |
| Sprache: | English |
| Veröffentlicht: |
1981
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| Zugriff auf das übergeordnete Werk: | Mathematics of Operations Research |
| Schlagworte: | Bargaining Pareto-optimality Multiattribute utility theory Mathematics Behavioral sciences Social sciences |
| Zusammenfassung: | A set of n players is to bargain over which one of m possible outcomes will be chosen. The preference of outcome i to player j is assumed to be a random variable with all preference rankings equally likely and without ties. This would arise in case the payoffs are chosen as independent samplings from a continuous distribution F<sub>j</sub>. The mean and distribution of the number of outcomes in the Pareto-optimal set are calculated for finite m. As m → ∞ the mean is asymptotic to <tex-math>$({\rm log}\ m+0.577)^{n-1}/(n-1)$</tex-math>! and for n = 2, m → ∞, the distribution approaches the normal distribution. The results are also applied to a problem in multiattribute utility theory. Suppose we wish to select an individual with high values on two personal attributes that are independent and continuously measurable. Of a world population of four billion, the efficient set would have an expectation of 22.7 individuals. |
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| ISSN: | 15265471 |