Two-Person Cake-Cutting: The Optimal Number of Cuts
21 Pages Posted: 22 Oct 2011
Date Written: October 20, 2011
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: Suggested Citation