Mechanism Design without Money for Fair Allocations

TL;DR

This paper investigates strategy-proof mechanisms for fair resource allocation without money, highlighting impossibility results for certain fairness notions and proposing a strategy-proof mechanism for single-minded agents.

Contribution

It demonstrates the impossibility of truthful mechanisms for EFX and existing EF1 algorithms, and introduces a strategy-proof serial dictatorship mechanism for single-minded agents.

Findings

No truthful mechanisms for EFX exist.

Existing EF1 algorithms are manipulable.

Serial Dictatorship is strategy-proof for single-minded agents.

Abstract

Fairness is well studied in the context of resource allocation. Researchers have proposed various fairness notions like envy-freeness (EF), and its relaxations, proportionality and max-min share (MMS). There is vast literature on the existential and computational aspects of such notions. While computing fair allocations, any algorithm assumes agents' truthful reporting of their valuations towards the resources. Whereas in real-world web-based applications for fair division, the agents involved are strategic and may manipulate for individual utility gain. In this paper, we study strategy-proof mechanisms without monetary transfer, which satisfies the various fairness criteria. We know that for additive valuations, designing truthful mechanisms for EF, MMS and proportionality is impossible. Here we show that there cannot be a truthful mechanism for EFX and the existing algorithms for EF1 are manipulable. We then study the particular case of single-minded agents. For this case, we provide a Serial Dictatorship Mechanism that is strategy-proof and satisfies all the fairness criteria except EF.