Plant-and-Steal: Truthful Fair Allocations via Predictions

TL;DR

This paper introduces a learning-augmented truthful mechanism for fair allocation of indivisible goods, achieving near-optimal MMS approximations with predictions, and demonstrating robustness and consistency through theoretical and experimental analysis.

Contribution

It proposes a novel prediction-based framework for truthful MMS allocation mechanisms, balancing accuracy and robustness, with new bounds and mechanisms for two and multiple agents.

Findings

Achieves 2-approximation with accurate predictions for two agents.

Maintains a near-optimal approximation when predictions are inaccurate.

Experimental results validate the theoretical robustness and consistency.

Abstract

We study truthful mechanisms for approximating the Maximin-Share (MMS) allocation of agents with additive valuations for indivisible goods. Algorithmically, constant factor approximations exist for the problem for any number of agents. When adding incentives to the mix, a jarring result by Amanatidis, Birmpas, Christodoulou, and Markakis [EC 2017] shows that the best possible approximation for two agents and $m$ items is $\lfloor \frac{m}{2} \rfloor$. We adopt a learning-augmented framework to investigate what is possible when some prediction on the input is given. For two agents, we give a truthful mechanism that takes agents' ordering over items as prediction. When the prediction is accurate, we give a $2$-approximation to the MMS (consistency), and when the prediction is off, we still get an $\lceil \frac{m}{2} \rceil$-approximation to the MMS (robustness). We further show that the mechanism's performance degrades gracefully in the number of ``mistakes" in the prediction; i.e., we interpolate (up to constant factors) between the two extremes: when there are no mistakes, and when there is a maximum number of mistakes. We also show an impossibility result on the obtainable consistency for mechanisms with finite robustness. For the general case of $n\ge 2$ agents, we give a 2-approximation mechanism for accurate predictions, with relaxed fallback guarantees. Finally, we give experimental results which illustrate when different components of our framework, made to insure consistency and robustness, come into play.