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We study fair division of indivisible goods under the maximin share (MMS) fairness criterion in settings where agents are grouped into a small number of types, with agents within each type having identical valuations. For the special case of a single type, an exact MMS allocation is always guaranteed to exist. However, for two or more distinct agent types, exact MMS allocations do not always exist, shifting the focus to establishing the existence of approximate-MMS allocations. A series of works over the last decade has resulted in the best-known approximation guarantee of 3/4 + 3/3836. In this paper, we improve the approximation guarantees for settings where agents are grouped into two or three types, a scenario that arises in many practical settings. Specifically, we present novel algorithms that guarantee a 4/5-MMS allocation for two agent types and a 16/21-MMS allocation for three agent types. Our approach leverages the MMS partition of the majority type and adapts it to provide improved fairness guarantees for all types.
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Fairness Does Not Imply Satisfaction (Student Abstract)
Fair division is a subfield of multiagent systems that is concerned with object distribution. When objects are indivisible, the Maximin Share Guarantee (MMS) is a desirable fairness notion; however, it is not guaranteed to exist. While MMS allocations may not always exist, a relaxation of MMS is guaranteed to exist. We show that there exists a family of instances for which this relaxation fails to guarantee the MMS value for all but a small constant number of agents.
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- PAR ID:
- 10281472
- Date Published:
- Journal Name:
- Proceedings of the AAAI Conference on Artificial Intelligence
- Volume:
- 34
- Issue:
- 10
- ISSN:
- 2159-5399
- Page Range / eLocation ID:
- 13911 to 13912
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript
- Journal Article:
- https://doi.org/10.1609/aaai.v34i10.7228
