Closing Gaps in Asymptotic Fair Division

04/12/2020 ∙ by Pasin Manurangsi, et al. ∙ 0

We study a resource allocation setting where m discrete items are to be divided among n agents with additive utilities, and the agents' utilities for individual items are drawn at random from a probability distribution. Since common fairness notions like envy-freeness and proportionality cannot always be satisfied in this setting, an important question is when allocations satisfying these notions exist. In this paper, we close several gaps in the line of work on asymptotic fair division. First, we prove that the classical round-robin algorithm is likely to produce an envy-free allocation provided that m=Ω(nlog n/loglog n), matching the lower bound from prior work. We then show that a proportional allocation exists with high probability as long as m≥ n, while an allocation satisfying envy-freeness up to any item (EFX) is likely to be present for any relation between m and n. Finally, we consider a related setting where each agent is assigned exactly one item and the remaining items are left unassigned, and show that the transition from non-existence to existence with respect to envy-free assignments occurs at m=en.

READ FULL TEXT
POST COMMENT

Comments

There are no comments yet.

Authors

page 1

page 2

page 3

page 4

This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.