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One of the most important topics in discrete fair division is whether an EFXallocation exists for any instance. Although the existence of EFX allocationsis a standing open problem for both goods and chores, the understanding of theexistence of EFX allocations for chores is less established compared to goods.We study the existence of EFX allocation for chores under the assumption thatall agent's cost functions are additive. Specifically, we show the existence ofEFX allocations for the following three cases: (i) the number of chores is atmost twice the number of agents, (ii) the cost functions of all agents exceptfor one are identical ordering, and (iii) the number of agents is three andeach agent has a personalized bi-valued cost function. Furthermore, we providea polynomial time algorithm to find an EFX allocation for each case.

EFX Allocations for Indivisible Chores: Matching-Based Approach