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Can I read An Algorithm For Super Envy-Free Cake Division on EtoBox?
An Algorithm For Super Envy-Free Cake Division by William A. Webb is a Mathematics article available to read on EtoBox.
What is An Algorithm For Super Envy-Free Cake Division about?
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 ,,..., X,} of X such that P, is satisfied to receive X , under some definition of fairness. The original problem introduced by Steinhaus in 1946 asked for a simple fair assignment where p i ( X j ) 2 l/n whenever 1 I i I n [23]. Other common criteria for fairness include strongly fair assignment where p j ( X i ) > l / n whenever 1 I i I n , envy-free where p i ( X , ) 2 p i ( X j ) whenever 1 I i, j I n and strongly envy-free where p,(X,) > p , ( X j ) whenever 1 I i, j I n and i # j . Recently, Barbanel introduced the condition of super envy-free where p i ( X , ) > l/n and p , ( X j ) < l/n whenever 1 5 i, j 5 n and i f j 131. Barbanel proved that a super envy-free partition exists if and only if the measures are linearly independent, that is c1 p1 + ...
Who reads An Algorithm For Super Envy-Free Cake Division?
It is typically read by researchers, students, and practitioners in Mathematics.
- Author
- William A. Webb
- Publisher
- Elsevier Science; Elsevier ; Elsevier Inc.; Elsevier BV (ISSN 0022-247X)
- Published
- 1999
- Language
- EN
- Field
- Mathematics (Physical Sciences)