Plant-and-Steal: Truthful Fair Allocations via Predictions

We study truthful mechanisms for approximating the Maximin-Share (MMS) value 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 ⌊^m/₂ ⌋. We adopt a learning-augmented framework to investigate what is possible when a 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, our mechanism gives a 2-approximation to the MMS (consistency), and when the prediction is off, our mechanism still obtains an ⌈^m/₂ ⌉- 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 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 ≥ 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 ensure consistency and robustness, come into play.