A characterization of Pareto surfaces

Authors:
Louis J. Billera and Robert E. Bixby

Journal:
Proc. Amer. Math. Soc. **41** (1973), 261-267

MSC:
Primary 90D12; Secondary 90D15

MathSciNet review:
0325163

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

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Additional Information

DOI:
http://dx.doi.org/10.1090/S0002-9939-1973-0325163-1

Keywords:
Pareto surface,
concave function,
utility function,
economic market,
trading economy,
game without side-payments,
convex set

Article copyright:
© Copyright 1973
American Mathematical Society