Maximin share and minimax envy in fair-division problems |
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Authors: | Marco Dall'Aglio Theodore P Hill |
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Institution: | a Dipartimento di Scienze, Universitá G. d'Annunzio, Viale Pindaro 42, 65127 Pescara, Italy b School of Mathematics, Georgia Institute of Technology, Atlanta, GA 30332-0160, USA |
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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. |
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Keywords: | Fair-division Cake-cutting Maximin share Minimax envy Envy-free Optimal partition Equitable partition |
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