EFX Allocations for Agents Who Refine a Common Valuation, and a Path-Following Reduction of the EFX Problem

This paper studies the existence of Envy-Free up to any item (EFX) allocations of indivisible goods for additive valuations. We investigate structural properties of EFX allocations and introduce a comprehensive framework consisting of a constructive proof for a refined common valuation case, alongside a novel reduction algorithm and extensive exact computations for multiple agents and goods. The full text and specific methodology are restricted during the initial peer-review and validation phase.