EFX Exists for Three Types of Agents

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.