Truthful Cake Sharing

TL;DR

This paper explores a fair and truthful mechanism design for a public goods variant of cake sharing, focusing on strategic agents with piecewise uniform utilities, and identifies conditions for optimal solutions.

Contribution

It introduces a truthful leximin mechanism that maximizes egalitarian welfare and analyzes the truthfulness of maximum Nash welfare solutions in this setting.

Findings

Leximin solution is truthful and maximizes egalitarian welfare.

Maximum Nash welfare is truthful for two agents but not in general.

Blocking access is crucial for mechanism truthfulness; without it, some mechanisms are impossible.

Abstract

The classic cake cutting problem concerns the fair allocation of a heterogeneous resource among interested agents. In this paper, we study a public goods variant of the problem, where instead of competing with one another for the cake, the agents all share the same subset of the cake which must be chosen subject to a length constraint. We focus on the design of truthful and fair mechanisms in the presence of strategic agents who have piecewise uniform utilities over the cake. On the one hand, we show that the leximin solution is truthful and moreover maximizes an egalitarian welfare measure among all truthful and position oblivious mechanisms. On the other hand, we demonstrate that the maximum Nash welfare solution is truthful for two agents but not in general. Our results assume that mechanisms can block each agent from accessing parts that the agent does not claim to desire; we provide an impossibility result when blocking is not allowed.