Does envy-freeness up to any good (EFX) always exist for indivisible item allocation?
An allocation is EFX if no agent envies another agent after removing any single item from the other agent's bundle. This is a central open problem in fair division.
Known results: - EFX exists for 2 agents (trivial) - EFX exists for 3 agents (Chaudhury et al., 2020) - EFX exists when there are only 2 types of items - EFX exists for identical valuations - EFX exists for restricted additive valuations in various settings
The general case for n ≥ 4 agents with arbitrary monotone valuations remains open.