Guarantees in Fair Division: General or Monotone Preferences

• 成果类型: Article
• 署名作者: Bogomolnaia, Anna; Moulin, Herve
• 署名单位: University of Glasgow; Centre National de la Recherche Scientifique (CNRS)
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• DOI: 10.1287/moor.2022.1255
• 发表日期: 2023
• 页码: 160-176
• 关键词: cake; cut

摘要

When dividing a manna Omega 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.