Finding Fair Allocations under Budget Constraints Article Swipe
Siddharth Barman
,
Arindam Khan
,
Sudarshan Shyam
,
Kidambi Sreenivas
·
YOU?
·
· 2023
· Open Access
·
· DOI: https://doi.org/10.1609/aaai.v37i5.25681
YOU?
·
· 2023
· Open Access
·
· DOI: https://doi.org/10.1609/aaai.v37i5.25681
We study the fair allocation of indivisible goods among agents with identical, additive valuations but individual budget constraints. Here, the indivisible goods--each with a specific size and value--need to be allocated such that the bundle assigned to each agent is of total size at most the agent's budget. Since envy-free allocations do not necessarily exist in the indivisible goods context, compelling relaxations--in particular, the notion of envy-freeness up to k goods (EFk)--have received significant attention in recent years. In an EFk allocation, each agent prefers its own bundle over that of any other agent, up to the removal of k goods, and the agents have similarly bounded envy against the charity (which corresponds to the set of all unallocated goods). It has been shown in prior work that an allocation that satisfies the budget constraints and maximizes the Nash social welfare is 1/4-approximately EF1. However, the computation (or even existence) of exact EFk allocations remained an intriguing open problem. We make notable progress towards this by proposing a simple, greedy, polynomial-time algorithm that computes EF2 allocations under budget constraints. Our algorithmic result implies the universal existence of EF2 allocations in this fair division context. The analysis of the algorithm exploits intricate structural properties of envy-freeness. Interestingly, the same algorithm also provides EF1 guarantees for important special cases. Specifically, we settle the existence of EF1 allocations for instances in which: (i) the value of each good is proportional to its size, (ii) all the goods have the same size, or (iii) all the goods have the same value. Our EF2 result even extends to the setting wherein the goods' sizes are agent specific.
Related Topics
Concepts
Bundle
Context (archaeology)
Mathematical economics
Bounded function
Budget constraint
Value (mathematics)
Set (abstract data type)
Exploit
Fair division
Simple (philosophy)
Computer science
Economics
Microeconomics
Mathematics
Machine learning
Philosophy
Composite material
Biology
Epistemology
Paleontology
Programming language
Materials science
Mathematical analysis
Computer security
Metadata
- Type
- article
- Language
- en
- Landing Page
- https://doi.org/10.1609/aaai.v37i5.25681
- https://ojs.aaai.org/index.php/AAAI/article/download/25681/25453
- OA Status
- diamond
- Cited By
- 14
- References
- 50
- Related Works
- 10
- OpenAlex ID
- https://openalex.org/W4382239849
All OpenAlex metadata
Raw OpenAlex JSON
- OpenAlex ID
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https://openalex.org/W4382239849Canonical identifier for this work in OpenAlex
- DOI
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https://doi.org/10.1609/aaai.v37i5.25681Digital Object Identifier
- Title
-
Finding Fair Allocations under Budget ConstraintsWork title
- Type
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articleOpenAlex work type
- Language
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enPrimary language
- Publication year
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2023Year of publication
- Publication date
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2023-06-26Full publication date if available
- Authors
-
Siddharth Barman, Arindam Khan, Sudarshan Shyam, Kidambi SreenivasList of authors in order
- Landing page
-
https://doi.org/10.1609/aaai.v37i5.25681Publisher landing page
- PDF URL
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https://ojs.aaai.org/index.php/AAAI/article/download/25681/25453Direct link to full text PDF
- Open access
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YesWhether a free full text is available
- OA status
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diamondOpen access status per OpenAlex
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https://ojs.aaai.org/index.php/AAAI/article/download/25681/25453Direct OA link when available
- Concepts
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Bundle, Context (archaeology), Mathematical economics, Bounded function, Budget constraint, Value (mathematics), Set (abstract data type), Exploit, Fair division, Simple (philosophy), Computer science, Economics, Microeconomics, Mathematics, Machine learning, Philosophy, Composite material, Biology, Epistemology, Paleontology, Programming language, Materials science, Mathematical analysis, Computer securityTop concepts (fields/topics) attached by OpenAlex
- Cited by
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14Total citation count in OpenAlex
- Citations by year (recent)
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2025: 7, 2024: 3, 2023: 4Per-year citation counts (last 5 years)
- References (count)
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50Number of works referenced by this work
- Related works (count)
-
10Other works algorithmically related by OpenAlex
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