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Article
Maximin Share and Minimax Envy in Fair-Division Problems
Journal of Mathematical Analysis and Applications
  • Marco Dall'Aglio, Universita G. d'Annunzio
  • Theodore P. Hill, Georgia Institute of Technology
Publication Date
1-1-2003
Abstract

For fair-division or cake-cutting problems with value functions which are normalized positive measures (i.e., the values are probability measures) maximin-share and minimax-envy inequalities are derived for both continuous and discrete measures. The tools used include classical and recent basic convexity results, as well as ad hoc constructions. Examples are given to show that the envy-minimizing criterion is not Pareto optimal, even if the values are mutually absolutely continuous. In the discrete measure case, sufficient conditions are obtained to guarantee the existence of envy-free partitions.

Citation Information
Marco Dall'Aglio and Theodore P. Hill. "Maximin Share and Minimax Envy in Fair-Division Problems" Journal of Mathematical Analysis and Applications Vol. 281 Iss. 1 (2003) p. 346 - 361
Available at: http://works.bepress.com/tphill/14/