Chore Cutting: Envy and Truth

TL;DR

This paper investigates the existence of truthful envy-free mechanisms for dividing divisible bad resources among strategic agents, proving several impossibility results under various constraints and valuation scenarios.

Contribution

It establishes fundamental impossibility results for deterministic truthful envy-free mechanisms in the context of bad resource division with strategic agents.

Findings

No deterministic truthful envy-free mechanism exists for connected-piece scenarios.

Deterministic truthful dictatorship mechanisms cannot satisfy envy-freeness.

Impossibility results hold even under non-wasteful constraints.

Abstract

We study the fair division of divisible bad resources with strategic agents who can manipulate their private information to get a better allocation. Within certain constraints, we are particularly interested in whether truthful envy-free mechanisms exist over piecewise-constant valuations. We demonstrate that no deterministic truthful envy-free mechanism can exist in the connected-piece scenario, and the same impossibility result occurs for hungry agents. We also show that no deterministic, truthful dictatorship mechanism can satisfy the envy-free criterion, and the same result remains true for non-wasteful constraints rather than dictatorship. We further address several related problems and directions.