Chore Cutting: Envy and Truth
This addresses fairness and incentive issues in resource allocation for strategic agents, though it appears incremental as it extends impossibility results to specific constraints.
The paper tackles the problem of fair division of divisible bad resources with strategic agents who can manipulate private information, showing that no deterministic truthful envy-free mechanisms exist under piecewise-constant valuations in connected-piece scenarios or for hungry agents, and that deterministic truthful dictatorship mechanisms also fail to satisfy envy-freeness.
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.