Almost Group Envy-free Allocation of Indivisible Goods and Chores
This addresses fairness in multi-agent resource allocation for scenarios with mixed utilities, but it is incremental as it builds on existing group envy-freeness concepts.
The paper tackled the problem of fair allocation of indivisible goods and chores by introducing stronger and relaxed versions of group envy-freeness, specifically GEF1, and designed polynomial-time algorithms to compute GEF1 allocations for two classes of additive utilities, while proving that checking GEF1 is coNP-complete.
We consider a multi-agent resource allocation setting in which an agent's utility may decrease or increase when an item is allocated. We take the group envy-freeness concept that is well-established in the literature and present stronger and relaxed versions that are especially suitable for the allocation of indivisible items. Of particular interest is a concept called group envy-freeness up to one item (GEF1). We then present a clear taxonomy of the fairness concepts. We study which fairness concepts guarantee the existence of a fair allocation under which preference domain. For two natural classes of additive utilities, we design polynomial-time algorithms to compute a GEF1 allocation. We also prove that checking whether a given allocation satisfies GEF1 is coNP-complete when there are either only goods, only chores or both.