On the structure of Pareto optimal cake partitions

We study Pareto optimal partitions of a "cake" among n players. Each player uses a countably additive non-atomic probability measure to evaluate the s ize of pieces of cake. We present two geometric pictures appropriate for th is study and consider the connection between these pictures and the maximiz ation of convex combinations of measures, which we studied in Barbanel and Zwicker [Barbanel, J.B., Zwicker, W., 1997. Two applications of a theorem o f Dvoretsky, Wald, and Wolfovitz to cake division. Theory and Decision 43, 203-207]. (C) 2000 Elsevier Science S.A. All rights reserved.