EFX
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Related Articles from SNS
EFX for Additive Chores: Nonexistence, Pareto Incompatibility, and Bi-Valued Existence
arXiv:2606.08872v1 Announce Type: new Abstract: We consider the fair division problem of indivisible chores and resolve the long-standing open problem for the existence of EFX allocations with additive cost functions. We show that, even for tri-valued additive cost functions, for every $n\geq 4$, there exists an instance with $n$ agents where no EFX allocation exists. Our counterexample only uses three types of chores, which is also tight on the number of types, as an EFX allocation is known...
Best-of-Both-Worlds Fairness of the Envy-Cycle-Elimination Algorithm
arXiv:2410.08986v2 Announce Type: replace Abstract: We consider the problem of fairly dividing indivisible goods among agents with additive valuations. It is known that an Epistemic EFX and $2/3$-MMS allocation can be obtained using the Envy-Cycle-Elimination (ECE) algorithm. In this work, we explore whether this algorithm can be randomized to also ensure ex-ante proportionality.
Generalized binary utility functions and fair allocations
arXiv:2109.08461v2 Announce Type: replace Abstract: The problem of finding envy-free allocations of indivisible goods can not always be solved; therefore, it is common to study some relaxations such as envy-free up to one good (EF1). Another property of interest for efficiency of an allocation is the Pareto Optimality (PO). Under additive utility functions, it is possible to find allocations EF1 and PO using Nash social welfare.