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Two-person cake-cutting: the optimal number of cuts

By Julius B. Barbanel and Steven J. Brams

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.

Topics: D63 - Equity, Justice, Inequality, and Other Normative Criteria and Measurement, D30 - General, D74 - Conflict; Conflict Resolution; Alliances, C61 - Optimization Techniques; Programming Models; Dynamic Analysis, D61 - Allocative Efficiency; Cost-Benefit Analysis, C72 - Noncooperative Games
Year: 2011
DOI identifier: 10.2139/ssrn.1946895
OAI identifier: oai:mpra.ub.uni-muenchen.de:34263

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