Sublinear Approximation Algorithm for Nash Social Welfare with XOS Valuations Article Swipe
Siddharth Barman
,
Anand Krishna
,
Pooja Kulkarni
,
Shivika Narang
·
YOU?
·
· 2024
· Open Access
·
· DOI: https://doi.org/10.4230/lipics.itcs.2024.8
YOU?
·
· 2024
· Open Access
·
· DOI: https://doi.org/10.4230/lipics.itcs.2024.8
We study the problem of allocating indivisible goods among n agents with the objective of maximizing Nash social welfare (NSW). This welfare function is defined as the geometric mean of the agents' valuations and, hence, it strikes a balance between the extremes of social welfare (arithmetic mean) and egalitarian welfare (max-min value). Nash social welfare has been extensively studied in recent years for various valuation classes. In particular, a notable negative result is known when the agents' valuations are complement-free and are specified via value queries: for XOS valuations, one necessarily requires exponentially many value queries to find any sublinear (in n) approximation for NSW. Indeed, this lower bound implies that stronger query models are needed for finding better approximations. Towards this, we utilize demand oracles and XOS oracles; both of these query models are standard and have been used in prior work on social welfare maximization with XOS valuations. We develop the first sublinear approximation algorithm for maximizing Nash social welfare under XOS valuations, specified via demand and XOS oracles. Hence, this work breaks the O(n)-approximation barrier for NSW maximization under XOS valuations. We obtain this result by developing a novel connection between NSW and social welfare under a capped version of the agents' valuations. In addition to this insight, which might be of independent interest, this work relies on an intricate combination of multiple technical ideas, including the use of repeated matchings and the discrete moving knife method. In addition, we partially complement the algorithmic result by showing that, under XOS valuations, an exponential number of demand and XOS queries are necessarily required to approximate NSW within a factor of (1 - 1/e).
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Metadata
- Type
- preprint
- Language
- en
- Landing Page
- https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2024.8
- OA Status
- green
- Cited By
- 4
- References
- 26
- Related Works
- 20
- OpenAlex ID
- https://openalex.org/W3203587481
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- OpenAlex ID
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https://openalex.org/W3203587481Canonical identifier for this work in OpenAlex
- DOI
-
https://doi.org/10.4230/lipics.itcs.2024.8Digital Object Identifier
- Title
-
Sublinear Approximation Algorithm for Nash Social Welfare with XOS ValuationsWork title
- Type
-
preprintOpenAlex work type
- Language
-
enPrimary language
- Publication year
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2024Year of publication
- Publication date
-
2024-01-01Full publication date if available
- Authors
-
Siddharth Barman, Anand Krishna, Pooja Kulkarni, Shivika NarangList of authors in order
- Landing page
-
https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2024.8Publisher landing page
- Open access
-
YesWhether a free full text is available
- OA status
-
greenOpen access status per OpenAlex
- OA URL
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https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2024.8Direct OA link when available
- Concepts
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Sublinear function, Valuation (finance), Social Welfare, Mathematical economics, Welfare, Maximization, Value (mathematics), Nash equilibrium, Upper and lower bounds, Mathematics, Microeconomics, Economics, Combinatorics, Statistics, Finance, Market economy, Political science, Mathematical analysis, LawTop concepts (fields/topics) attached by OpenAlex
- Cited by
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4Total citation count in OpenAlex
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2025: 1, 2024: 2, 2023: 1Per-year citation counts (last 5 years)
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26Number of works referenced by this work
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20Other works algorithmically related by OpenAlex
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