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We investigate the existence of fair and efficient allocations of indivisible chores to asymmetric agents who have unequal entitlements or weights. We consider the fairness notion of weighted envy-freeness up to one chore (wEF1) and the efficiency notion of Pareto-optimality (PO). The existence of EF1 and PO allocations of chores to symmetric agents is a major open problem in discrete fair division, and positive results are known only for certain structured instances. In this paper, we study this problem for a more general setting of asymmetric agents and show that an allocation that is wEF1 and PO exists and can be computed in polynomial time for instances with:- Three types of agents where agents with the same type have identical preferences but can have different weights. - Two types of choresFor symmetric agents, our results establish that EF1 and PO allocations exist for three types of agents and also generalize known results for three agents, two types of agents, and two types of chores. Our algorithms use a weighted picking sequence algorithm as a subroutine; we expect this idea and our analysis to be of independent interest.
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Almost Envy-Free Allocations of Indivisible Goods or Chores with Entitlements
We here address the problem of fairly allocating indivisible goods or chores to n agents with weights that define their entitlement to the set of indivisible resources. Stemming from well-studied fairness concepts such as envy-freeness up to one good (EF1) and envy-freeness up to any good (EFX) for agents with equal entitlements, we present, in this study, the first set of impossibility results alongside algorithmic guarantees for fairness among agents with unequal entitlements.Within this paper, we expand the concept of envy-freeness up to any good or chore to the weighted context (WEFX and XWEF respectively), demonstrating that these allocations are not guaranteed to exist for two or three agents. Despite these negative results, we develop a WEFX procedure for two agents with integer weights, and furthermore, we devise an approximate WEFX procedure for two agents with normalized weights. We further present a polynomial-time algorithm that guarantees a weighted envy-free allocation up to one chore (1WEF) for any number of agents with additive cost functions. Our work underscores the heightened complexity of the weighted fair division problem when compared to its unweighted counterpart.
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- PAR ID:
- 10567359
- Publisher / Repository:
- AAAI
- Date Published:
- Journal Name:
- Proceedings of the AAAI Conference on Artificial Intelligence
- Volume:
- 38
- Issue:
- 9
- ISSN:
- 2159-5399
- Page Range / eLocation ID:
- 9901 to 9908
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1609/AAAI.V38I9.28851
