In this paper, we study the problem of finding an envy-free allocation of indivisible goods among multiple agents. EFX, which stands for envy-freeness up to any good, is a well-studied relaxation of the envy-free allocation problem and has been shown to exist for specific scenarios. For instance, EFX is known to exist when there are only three agents [Chaudhury et al, EC 2020], and for any number of agents when there are only two types of valuations [Mahara, Discret. Appl. Math 2023]. We show that EFX allocations exist for any number of agents when there are at most three types of additive valuations.

翻译：本文研究了在多个代理之间分配不可分割物品的无嫉妒分配问题。EFX（即任意物品上的无嫉妒性）是无嫉妒分配问题的一个经过深入研究的松弛条件，并已在特定场景中被证明存在。例如，已知当仅有三个代理时 EFX 存在 [Chaudhury et al, EC 2020]，并且当仅有两种估值类型时，对于任意数量的代理 EFX 也存在 [Mahara, Discret. Appl. Math 2023]。我们证明，当至多存在三种可加估值类型时，对于任意数量的代理，EFX 分配均存在。