On the Price of Fairness in the Connected Discrete Cake Cutting Problem

Ankang Sun, Bo Li

Abstract: Discrete cake cutting is a fundamental model in fair resource allocation where the indivisible resources are located on a path. It is well motivated that, in reality, each agent is interested in receiving a contiguous block of items. An important question therein is to understand the economic efficiency loss by restricting the allocations to be fair, which is quantified as price of fairness (PoF). Informally, PoF is the worst-case ratio between the unconstrained optimal welfare and the optimal welfare achieved by fair allocations. Suksompong [Discret. Appl. Math., 2019] has studied this problem, where fairness is measured by the ideal criteria such as proportionality (PROP). A PROP allocation, however, may not exist in discrete cake cutting settings. Therefore, in this work, we revisit this problem and focus on the relaxed notions whose existence is guaranteed. We study both utilitarian and egalitarian welfare, and our results show significant differences between the PoF of guaranteed fairness notions and that of the ideal notions.