[alpha]-maxmin solutions to fair division problems and the structure of the set of Pareto utility profiles

Abstract

A simple proof of the equivalence of Pareto optimality plus positiveness and [alpha]-maxmin optimality, dispensing with the assumption of closedness of the utility possibility set, is given. Also the structure of the set of Pareto optimal utility profiles is studied.Fair division Non-atomic probability space Pareto optimality [alpha]-equitability [alpha]-maxmin optimality