We study non-atomic congestion games on parallel-link networks with polynomial latencies. We investigate the power of machine-learned predictions in the design of coordination mechanisms aimed at minimizing the impact of selfishness. Our main results demonstrate that enhancing coordination mechanisms with simple advice on the input rate can optimize the social cost whenever the advice is accurate (consistency ), while only incurring minimal losses even when the predictions are arbitrarily inaccurate (bounded robustness ). Moreover, we provide a full characterization of consistent mechanisms, which holds for all monotone cost functions, and show that our proposed mechanism is optimal with respect to robustness. We further explore the notion of error-tolerance within this context, i.e., we provide an approximation guarantee that degrades smoothly as a function of the prediction error, up to a predetermined threshold, while achieving a bounded robustness.

We study the problem of fairly allocating a set of indivisible items among a set of agents. We consider the notion of (approximate) maximin share (MMS) and we provide an improved lower bound of 1/2 (which is tight) for the case of subadditive valuations when the number of agents is at most four. We also provide a tight lower bound for the case of multiple agents, when they are equipped with one of two possible types of valuations. Moreover, we propose a new model that extends previously studied models in the area of fair division, which will hopefully give rise to further research. We demonstrate the usefulness of this model by employing it as a technical tool to derive our main result, and we provide a thorough analysis for this model for the case of three agents. Finally, we provide an improved impossibility result for the case of three submodular agents.

We study the problem of fairly allocating indivisible goods among agents which are equipped with leveled valuation functions. Such preferences, that have been studied before in economics and fair division literature, capture a simple and intuitive economic behavior; larger bundles are always preferred to smaller ones. We provide a fine-grained analysis for various subclasses of leveled valuations focusing on two extensively studied notions of fairness, (approximate) MMS and EFX. In particular, we present a general positive result, showing the existence of 2/3-MMS allocations under valuations that are both leveled and submodular. We also show how some of our ideas can be used beyond the class of leveled valuations; for the case of two submodular (not necessarily leveled) agents we show that there always exists a 2/3-MMS allocation, complementing a recent impossibility result. Then, we switch to the case of subadditive and fractionally subadditive leveled agents, where we are able to show tight (lower and upper) bounds of 1/2 on the approximation factor of MMS. Moreover, we show the existence of exact EFX allocations under general leveled valuations via a simple protocol that in addition satisfies several natural economic properties. Finally, we take a mechanism design approach and we propose protocols that are both truthful and approximately fair under leveled valuations. • We study various notions of fairness under leveled valuations. • Positive results regarding the existence of approximate MMS allocations. • We show the existence of exact EFX allocations under leveled valuations. • We explore the interplay of fairness and incentive compatibility for this class of valuations and show positive results.