Cake cutting: Fair and square

Arbeitspapier

The classic fair cake-cutting problem [Steinhaus, 1948] is extended by introducing geometric constraints on the allocated pieces. Specifically, agents may demand to get their share as a square or a rectangle with a bounded length/width ratio. This is a plausible constraint in realistic cake-cutting applications, notably in urban and agricultural economics where the cake is land. Geometric constraints greatly affect the classic results of the fair division theory. The existence of a proportional division, giving each agent 1/n of his total cake value, is no longer guaranteed. We prove that it is impossible to guarantee each agent more than 1/(2n-1) of his total value. Moreover, we provide procedures implementing partially proportional division, giving each agent 1/(An-B) of his total value, where A and B are constants depending on the shape of the cake and its pieces. Fairness and social welfare implications of these procedures are analyzed in various scenarios.

Object Details

• Language: Englisch

References and Relationships

• Bibliographic citation: Series: Working Paper ; No. 2014-01

Classification and Topics

• Classification: Wirtschaft
• Subject: fair division ; cake cutting ; land division ; geometry ; non-additive utilities ; social welfare

Contributors, Places and Time

• Event: Geistige Schöpfung
• (who): Segal-Halevi, Erel ; Nitzan, Shmuel
• Event: Veröffentlichung
• (who): Bar-Ilan University, Department of Economics
• (where): Ramat-Gan
• (when): 2014

Further information

• Handle: http://hdl.handle.net/10419/96057
• Last update: 10.03.2025, 11:44 AM CET