On Truthful Mechanisms without Pareto-efficiency: Characterizations and Fairness

TL;DR

This paper characterizes strategy-proof, non-bossy, and neutral mechanisms for allocating indivisible goods without requiring Pareto-efficiency, revealing their uniqueness within certain preference classes.

Contribution

It proves that serial-quota mechanisms are the only strategy-proof, non-bossy, and neutral mechanisms for specific preference classes, even without Pareto-efficiency.

Findings

Serial-quota mechanisms are unique for strict ordinal preferences.

Results extend to cardinal preferences including additive valuations.

Negative implications for truthful mechanisms in fair allocation with additive valuations.

Abstract

We consider the problem of allocating heterogeneous and indivisible goods among strategic agents, with preferences over subsets of goods, when there is no medium of exchange. This model captures the well studied problem of fair allocation of indivisible goods. Serial-quota mechanisms are allocation mechanisms where there is a predefined order over agents, and each agent in her turn picks a predefined number of goods from the remaining goods. These mechanisms are clearly strategy-proof, non-bossy, and neutral. Are there other mechanisms with these properties? We show that for important classes of strict ordinal preferences (as lexicographic preferences, and as the class of all strict preferences), these are the only mechanisms with these properties. Importantly, unlike previous work, we can prove the claim even for mechanisms that are not Pareto-efficient. Moreover, we generalize these results to preferences that are cardinal, including any valuation class that contains additive valuations. We then derive strong negative implications of this result on truthful mechanisms for fair allocation of indivisible goods to agents with additive valuations.