Guarantees in Fair Division: General or Monotone Preferences

Anna Bogomolnaia (anna.bogomolnaia@univ-paris1.fr) and Herve Moulin
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Anna Bogomolnaia: HSE St Petersburg - Higher School of Economics - St Petersburg, University of Glasgow, CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique

Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) from HAL

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: fair division; divide and choose; guarantees; nonatomic utilities (search for similar items in EconPapers)
Date: 2022-04-08
New Economics Papers: this item is included in nep-des and nep-upt
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Published in Mathematics of Operations Research, 2022, 1, pp.1-602, C2. ⟨10.1287/moor.2022.1255⟩

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Related works:
Journal Article: Guarantees in Fair Division: General or Monotone Preferences (2023)
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)
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Persistent link: https://EconPapers.repec.org/RePEc:hal:cesptp:hal-03886828

DOI: 10.1287/moor.2022.1255

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