Plant-and-Steal: Truthful Fair Allocations via Predictions
Ilan Reuven Cohen, Alon Eden, Talya Eden, Arsen Vasilyan
TL;DR
This work investigates truthful mechanisms for approximately maximizing the Maximin Share (MMS) in settings with additive valuations over indivisible goods. By introducing a learning-augmented Plant-and-Steal framework, the authors exploit predictions to achieve strong consistency when predictions are accurate while preserving robust guarantees when predictions are noisy, with detailed treatment for both two-agent and general-$n$ scenarios. The core ideas combine prediction-driven allocations with a planting/stealing correction phase to preserve truthfulness and fairness guarantees, supported by analyses under various prediction models (ordering and non-ordering) and by experimental validation. The results establish tight (or near-tight) consistency–robustness tradeoffs, including space-efficient prediction schemes and recursive mechanisms for many agents, advancing practical truthful fair allocation with imperfect information. The framework integrates Round-Robin variants, water-filling, and cut-and-balance techniques to achieve practical performance guarantees in diverse prediction regimes.
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.