Chore Cutting: Envy and Truth
Mohammad Azharuddin Sanpui

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.
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Taxonomy
TopicsAuction Theory and Applications · Law, Economics, and Judicial Systems · Economic theories and models
