On a game theoretic notion of complexity for compact convex sets

Kalai, Ehud; Smorodinsky, Meir

doi:10.1090/S0002-9939-1975-0368707-8

Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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On a game theoretic notion of complexity for compact convex sets
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by Ehud Kalai and Meir Smorodinsky PDF

Proc. Amer. Math. Soc. 49 (1975), 416-420 Request permission

Abstract:

The notion of complexity for compact convex sets introduced by Billera and Bixby is considered. It is shown that for $n \geq 3$ there are sets in ${R^n}$ of complexity $n$. Also for $n = 3$ the maximal complexity is 3.

References

Louis J. Billera and Robert E. Bixby, A characterization of Pareto surfaces, Proc. Amer. Math. Soc. 41 (1973), 261–267. MR 325163, DOI 10.1090/S0002-9939-1973-0325163-1