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Title: Almost Envy-freeness, Envy-rank, and Nash Social Welfare Matchings
Award ID(s):
1822738
PAR ID:
10301041
Author(s) / Creator(s):
Date Published:
Journal Name:
Proceedings of the AAAI Conference on Artificial Intelligence
ISSN:
2159-5399
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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  1. ; ; ; (, NeurIPS'19)
  2. ; ; ; (, Proceedings of the AAAI Conference on Artificial Intelligence)
    We investigate the fair allocation of indivisible goods to agents with possibly different entitlements represented by weights. Previous work has shown that guarantees for additive valuations with existing envy-based notions cannot be extended to the case where agents have matroid-rank (i.e., binary submodular) valuations. We propose two families of envy-based notions for matroid-rank and general submodular valuations, one based on the idea of transferability and the other on marginal values. We show that our notions can be satisfied via generalizations of rules such as picking sequences and maximum weighted Nash welfare. In addition, we introduce welfare measures based on harmonic numbers, and show that variants of maximum weighted harmonic welfare offer stronger fairness guarantees than maximum weighted Nash welfare under matroid-rank valuations. 
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