The Number of Outcomes in the Pareto-Optimal Set of Discrete Bargaining Games

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...

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Veröffentlicht in:Mathematics of Operations Research. - Institute for Operations Research and the Management Sciences. - 6(1981), 4, Seite 571-578
1. Verfasser: O'Neill, Barry (VerfasserIn)
Format: Online-Aufsatz
Sprache:English
Veröffentlicht: 1981
Zugriff auf das übergeordnete Werk:Mathematics of Operations Research
Schlagworte:Bargaining Pareto-optimality Multiattribute utility theory Mathematics Behavioral sciences Social sciences
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520 |a 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. 
540 |a Copyright 1981 The Institute of Management Sciences 
650 4 |a Bargaining 
650 4 |a Pareto-optimality 
650 4 |a Multiattribute utility theory 
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