Guarantees in Fair Division: General or Monotone Preferences

Anna Bogomolnaia () and Herve Moulin
Additional contact information
Anna Bogomolnaia: Adam Smith Business School, University of Glasgow, Glasgow G128QQ, United Kingdom

Mathematics of Operations Research, 2023, vol. 48, issue 1, 160-176

Abstract: When dividing a “manna” Ω of private items (commodities, workloads, land, time slots) between n agents, the individual guarantee is the welfare each agent can secure in the worst case of other agents’ preferences and actions. If the manna is nonatomic and utilities are continuous (not necessarily monotone or convex) the minmax utility, that of our agent’s best share in the agent’s worst partition of the manna, is guaranteed by Kuhn’s generalization of divide and choose. The larger maxmin utility—of the agent’s worst share in the agent’s best partition—cannot be guaranteed even for two agents. If, for all agents, more manna is better than less (or less is better than more), the new bid and choose rules offer guarantees between minmax and maxmin by letting agents bid for the smallest (or largest) size of a share they find acceptable.

Keywords: Primary: 91B32; secondary: 55M20; fair division; divide and choose; guarantees; nonatomic utilities (search for similar items in EconPapers)
Date: 2023
References: Add references at CitEc
Citations:

Downloads: (external link)
http://dx.doi.org/10.1287/moor.2022.1255 (application/pdf)

Related works:
Working Paper: Guarantees in Fair Division: General or Monotone Preferences (2022)
Working Paper: Guarantees in Fair Division: General or Monotone Preferences (2022)
Working Paper: Guarantees in Fair Division: general or monotone preferences (2020)
Working Paper: Guarantees in Fair Division: general or monotone preferences (2020)
Working Paper: Guarantees in Fair Division: general or monotone preferences (2020)
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:inm:ormoor:v:48:y:2023:i:1:p:160-176

Access Statistics for this article

More articles in Mathematics of Operations Research from INFORMS Contact information at EDIRC.
Bibliographic data for series maintained by Chris Asher ().