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A Characterization of Pareto Surfaces

Louis J. Billera and Robert E. Bixby
Proceedings of the American Mathematical Society
Vol. 41, No. 1 (Nov., 1973), pp. 261-267
DOI: 10.2307/2038853
Stable URL: http://www.jstor.org/stable/2038853
Page Count: 7
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
A Characterization of Pareto Surfaces
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Abstract

Given n concave continuous functions ui defined over the unit m-cube Im, the corresponding attainable set V and Pareto surface P are defined. In the economic interpretation, V corresponds to the set of attainable utility outcomes realized through trading, and P the set of such outcomes for which no trader can attain more without another getting less. Sets of the form of V and P are characterized among all subsets of Rn. The notion of complexity (the smallest m for which a given V can be realized) is briefly discussed, as is the idea of a "market game".

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