Paper Info
Title
Approximation Algorithms for Maximin Fair Division
Abstract
We consider the problem of allocating indivisible goods fairly among n agents who have additive and submodular valuations for the goods. Our fairness guarantees are in terms of the maximin share, which is defined to be the maximum value that an agent can ensure for herself, if she were to partition the goods into n bundles, and then receive a minimum valued bundle. Since maximin fair allocations (i.e., allocations in which each agent gets at least her maximin share) do not always exist, prior work has focused on approximation results that aim to find allocations in which the value of the bundle allocated to each agent is (multiplicatively) as close to her maximin share as possible. In particular, Procaccia and Wang (2014) along with Amanatidis et al. (2015) have shown that under additive valuations, a 2/3-approximate maximin fair allocation always exists and can be found in polynomial time. We complement these results by developing a simple and efficient algorithm that achieves the same approximation guarantee. Furthermore, we initiate the study of approximate maximin fair division under submodular valuations. Specifically, we show that when the valuations of the agents are nonnegative, monotone, and submodular, then a 0.21-approximate maximin fair allocation is guaranteed to exist. In fact, we show that such an allocation can be efficiently found by using a simple round-robin algorithm. A technical contribution of the article is to analyze the performance of this combinatorial algorithm by employing the concept of multilinear extensions.
Year
DOI
Venue
2020
10.1145/3381525
ACM Transactions on Economics and Computation
Keywords
DocType
Volume
Fair division,maximin shares,multilinear extensions,submodular valuations
Journal
8
Issue
ISSN
Citations 
1
2167-8375
1
PageRank 
References 
Authors
0.36
0
2
Name
Order
Citations
PageRank
Siddharth Barman119926.26
Sanath Kumar Krishnamurthy211.37