On envy-free cake division
โ Scribed by Steven J Brams; Alan D Taylor
- Publisher
- Elsevier Science
- Year
- 1995
- Tongue
- English
- Weight
- 234 KB
- Volume
- 70
- Category
- Article
- ISSN
- 0097-3165
No coin nor oath required. For personal study only.
๐ SIMILAR VOLUMES
The standard mathematical setting for fair division problems begins with a cake X which is a compact subset of some Euclidean space and n players P,, . . . ,el each with an additive nonatomic probability measure p,,. . . , p,, on a a-algebra of measureable subsets of X , and asks for a partition { X
The minimal number of parallel cuts required to divide a cake into n pieces is n ร 1. A new 3person procedure, requiring two parallel cuts, is given that produces an envy-free division, whereby each person thinks he or she receives at least a tied-for-largest piece. An extension of this procedure le
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 ลฝ . Set,'' which we studied before 2000, J. Math. Eco