### Abstract

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

Original language | English (US) |
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Pages (from-to) | 416-420 |

Number of pages | 5 |

Journal | Proceedings of the American Mathematical Society |

Volume | 49 |

Issue number | 2 |

DOIs | |

State | Published - Jan 1 1975 |

### Keywords

- Compact convex sets
- Complexity
- Concave utility functions
- Market games

### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

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## Cite this

Kalai, E., & Smorodinsk, M. (1975). On a game theoretic notion of complexity for compact convex sets.

*Proceedings of the American Mathematical Society*,*49*(2), 416-420. https://doi.org/10.1090/S0002-9939-1975-0368707-8