An Improved Lower Bound for Maximin Share Allocations of Goods

09/13/2022

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by   Kevin Hsu, et al.

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The problem of fair division of indivisible goods has been receiving much attention recently. The prominent metric of envy-freeness can always be satisfied in the divisible goods setting (see for example <cit.>), but often cannot be satisfied in the indivisible goods setting. This has led to many relaxations thereof being introduced. We study the existence of maximin share (MMS) allocations, which is one such relaxation. Previous work has shown that MMS allocations are guaranteed to exist for all instances with n players and m goods if m ≤ n+4. We extend this guarantee to the case of m = n+5 and show that the same guarantee fails for m = n+6.