A characterization of α-maximin solutions of fair division problems

This paper investigates the problem of fair division of a measurable space among a finite number of individuals and characterizes some equity concepts when preferences of each individual are represented by a nonadditive set function on a σ-algebra. We show that if utility functions of individuals satisfy continuity from below and strict monotonicity, then positive Pareto optimality is equivalent to α-maximin optimality for some α in the unit simplex and Pareto-optimal α-equitability is equivalent to α-maximin optimality. These characterizations are novel in the literature.