The Efficiency of Fair Division with Connected Pieces

Abstract

The cake-cutting setting, in which a single heterogeneous good must be divided between multiple parties with different tastes, is a classic model for studying questions regarding fairness in resource allocation. In this work, we turn our attention to (economic) efficiency considerations in cake cutting, examining the possible trade-offs between meeting the fairness criteria, on the one hand, and maximizing social welfare, on the other. We focus on divisions that give each agent a single (contiguous) piece of the cake and provide tight bounds (or, in some cases, nearly tight) on the possible degradation in utilitarian and egalitarian welfare resulting from meeting the fairness requirements.