EFX∨MMS allocations can fail for three agents with submodular goods (8 items) or chores (7 items), but always exist for additive mixed items with at most three valuation types when one type is a singleton.
Guarantees in Fair Division: general or monotone preferences
1 Pith paper cite this work. Polarity classification is still indexing.
1
Pith paper citing it
abstract
To divide a "manna" {\Omega} of private items (commodities, workloads, land, time intervals) between n agents, the worst case measure of fairness is the welfare guaranteed to each agent, irrespective of others' preferences. If the manna is non atomic and utilities are continuous (not necessarily monotone or convex), we can guarantee the minMax utility: that of our agent's best share in her worst partition of the manna; and implement it by Kuhn's generalisation of Divide and Choose. The larger Maxmin utility -- of her worst share in her 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), our Bid & Choose rules implement guarantees between minMax and Maxmin by letting agents bid for the smallest (or largest) size of a share they find acceptable.
fields
cs.GT 1years
2026 1verdicts
CONDITIONAL 1representative citing papers
citing papers explorer
-
To EFX OR to MMS, That is the Question
EFX∨MMS allocations can fail for three agents with submodular goods (8 items) or chores (7 items), but always exist for additive mixed items with at most three valuation types when one type is a singleton.