  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.
