Abstract
One of the most important topics in discrete fair division is whether an EFX allocation exists for any instance. Although the existence of EFX allocations is a standing open problem for both goods and chores, the understanding of the existence of EFX allocations for chores is less established compared to goods. We study the existence of EFX allocation for chores under the assumption that all agents' cost functions are additive. Specifically, we design polynomial time algorithms for computing EFX allocations for the following three cases: (i) the number of chores is at most twice the number of agents, (ii) the cost functions of all agents except for one induce the same ordering, and (iii) the number of agents is three and each agent has a personalized bi-valued cost function.
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