Weighted fair division with matroid-rank valuations: Monotonicity and strategyproofness

Weighted Envy-Freeness for Submodular Valuations

“…3.3). Clean allocations are common in the study of matroid-rank valuations (Babaioff, Ezra, and Feige 2021a;Benabbou et al 2021;Barman and Verma 2022;Goko et al 2022;Suksompong and Teh 2023;Viswanathan and Zick 2023a,b). While clean allocations may be incomplete, achieving completeness along with certain properties under matroid-rank valuations can be surprisingly challenging-we refer to the discussion by Benabbou et al (2021, p. 21).…”

“…2 Note that the valuations in Example 1 are particularly simple: both agents have binary submodular valuations, that is, submodular valuations 3 in which the marginal gain from receiving any single good is either 0 or 1. Binary submodular valuations are also known as matroid-rank valuations, and have been studied in a number of recent fair division papers, mostly in the unweighted setting (Babaioff, Ezra, and Feige 2021a;Verma 2021, 2022;Benabbou et al 2021;Goko et al 2022;Suksompong and Teh 2023;Viswanathan and Zick 2023a,b). 4 Such valuations arise in settings such as the allocation of course slots to students, or apartments in public housing estates to ethnic groups (Benabbou et al 2021).…”

“…3 See the definition of submodularity in Section 2. 4 Exceptions are the recent works of Suksompong and Teh (2023) and Viswanathan and Zick (2023a), which deal with the weighted setting. In fact, Viswanathan and Zick (2023a) pointed out that the "main limitation" of their approach is that it cannot be used to achieve envy-based fairness properties; this is precisely the issue that we address in our paper.…”