Two-Person Cake-Cutting: The Optimal Number of Cuts

21 Pages Posted: 22 Oct 2011

See all articles by Julius B. Barbanel

Julius B. Barbanel

Union College

Steven J. Brams

New York University (NYU) - Wilf Family Department of Politics

Date Written: October 20, 2011

Abstract

A cake is a metaphor for a heterogeneous, divisible good. When two players divide such a good, there is always a perfect division — one that is efficient (Pareto-optimal), envy-free, and equitable — which can be effected with a finite number of cuts under certain mild conditions; this is not always the case when there are more than two players (Brams, Jones, and Klamler, 2011b). We not only establish the existence of such a division but also provide an algorithm for determining where and how many cuts must be made, relating it to an algorithm, “Adjusted Winner” (Brams and Taylor, 1996, 1999), that yields a perfect division of multiple homogenous goods.

Keywords: Cake-cutting, fair division, envy-freeness, adjusted winner, heterogeneous good

JEL Classification: C61, C72, D30, D61, D63, D74

Suggested Citation

Barbanel, Julius B. and Brams, Steven, Two-Person Cake-Cutting: The Optimal Number of Cuts (October 20, 2011). Available at SSRN: https://ssrn.com/abstract=1946895 or http://dx.doi.org/10.2139/ssrn.1946895

Julius B. Barbanel

Union College ( email )

Schenectady, NY 12308-3151
United States

Steven Brams (Contact Author)

New York University (NYU) - Wilf Family Department of Politics ( email )

Dept. of Politics
19 West 4th St., 2nd Fl.
New York, NY 10012
United States
212-998-8510 (Phone)
212-995-4184 (Fax)

HOME PAGE: http://politics.as.nyu.edu/object/stevenbrams.html

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