Truthful Fair Division without Free Disposal

TL;DR

This paper investigates fair division of resources without free disposal, presenting truthful and envy-free mechanisms for two agents with specific valuations, and exploring the limitations and bounds of such mechanisms for multiple agents.

Contribution

It introduces the first truthful, envy-free mechanism for cake cutting without free disposal for two agents with piecewise uniform valuations, and analyzes constraints and bounds for broader settings.

Findings

Existence of a truthful, envy-free mechanism for two agents with piecewise uniform valuations.

Non-existence of such mechanisms under certain additional constraints.

Bounds on efficiency for mechanisms satisfying various properties.

Abstract

We study the problem of fairly dividing a heterogeneous resource, commonly known as cake cutting and chore division, in the presence of strategic agents. While a number of results in this setting have been established in previous works, they rely crucially on the free disposal assumption, meaning that the mechanism is allowed to throw away part of the resource at no cost. In the present work, we remove this assumption and focus on mechanisms that always allocate the entire resource. We exhibit a truthful and envy-free mechanism for cake cutting and chore division for two agents with piecewise uniform valuations, and we complement our result by showing that such a mechanism does not exist when certain additional constraints are imposed on the mechanisms. Moreover, we provide bounds on the efficiency of mechanisms satisfying various properties, and give truthful mechanisms for multiple agents with restricted classes of valuations.