On the geometry of cake division

[摘要] We study partitions of a cake C among n players. Each player uses a countably additive non-atomic probability measure to evaluate the sizes of pieces of cake. If the players' measures are m(1), m(2), ..., m(n), then the Individual Pieces Set, which we studied before (2000, J. Math. Econom. 33, 401-424), is the set {(m(1)(P-1), m(2)(P-2), ..., m(n)(P-n)): [P-1, P-2, ..., P-n] is a partition of C}. We continue our study of this set here. Our motivating question is: What are the possible shapes of such sets? We give an exact characterization for n = 2, establish some partial results for n = 3, and close with open questions. (C) 2001 Elsevier Science.

[发布日期] 2001-12-15

[关键词] fair division;Pareto optimal