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Topological properties of the efficient point set

Author: Bezalel Peleg
Journal: Proc. Amer. Math. Soc. 35 (1972), 531-536
MSC: Primary 90A99; Secondary 54F05, 90D99
MathSciNet review: 0303916
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Abstract: Let y be a closed and convex subset of a Euclidean space. We prove that the set of efficient points of Y, $ M(Y)$, is contractible. Furthermore, if $ M(Y)$ is closed (compact) then it is a retract of a convex closed (compact) set. Our proof relies on the Arrow-Barankin-Blackwell Theorem. A new proof is supplied for that theorem.

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  • [1] K. J. Arrow, E. W. Barankin, and D. Blackwell, Admissible points of convex sets, Contributions to the theory of games, vol. 2, Annals of Mathematics Studies, no. 28, Princeton University Press, Princeton, N. J., 1953, pp. 87–91. MR 0054919
  • [2] David Gale, The theory of linear economic models, McGraw-Hill Book Co., Inc., New York-Toronto-London, 1960. MR 0115801
  • [3] Tjalling C. Koopmans, Analysis of production as an efficient combination of activities, Activity Analysis of Production and Allocation, Cowles Commission Monograph No. 13, John Wiley & Sons, Inc., New York, N. Y.; Chapman & Hall, Ltd., London, 1951, pp. 33–97. MR 0046017
  • [4] M. Kurz and M. Majumdar, Efficiency prices in infinite dimensional spaces: A synthesis (to appear).
  • [5] Mukul Majumdar, Some approximation theorems on efficiency prices for infinite programs, J. Econom. Theory 2 (1970), 399–410. MR 0449549
  • [6] Hukukane Nikaidô, Convex structures and economic theory, Mathematics in Science and Engineering, Vol. 51, Academic Press, New York-London, 1968. MR 0277233
  • [7] Bezalel Peleg, Efficiency prices for optimal consumption plans, J. Math. Anal. Appl. 29 (1970), 83–90. MR 0260408
  • [8] Bezalel Peleg, Efficiency prices for optimal consumption plans. II, Israel J. Math. 9 (1971), 222–234. MR 0277234
  • [9] Roy Radner, A note on maximal points of convex sets in 𝑙_{∞}, Proc. Fifth Berkeley Sympos. Math. Statist. and Probability (Berkeley, Calif., 1965/66) Univ. California Press, Berkeley, Calif., 1967, pp. 351–354. MR 0216276

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Article copyright: © Copyright 1972 American Mathematical Society