On the Geometry of Cake Division

✍ Scribed by Julius Barbanel

• Publisher: Elsevier Science
• Year: 2001
• Tongue: English
• Weight: 179 KB
• Volume: 264
• Category: Article
• ISSN: 0022-247X
• DOI: 10.1006/jmaa.2001.7687

✦ Synopsis

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 , m , . . . , m , then the ''Individual Pieces 1 2 n Ž . Set,'' which we studied before 2000, J. Math. Econom. 33, 401᎐424 , is the set ÄŽ Ž . Ž . Ž .. ² : 4 m P , m P , . . . , m P : P , P , . . . , P is a partition of C . We continue 1 1 2 2 n n 1 2 n 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 s 2, establish some partial results for n s 3, and close with open questions.