Mahmoud Fouz

Complete EFX Allocations Exist for Four Additive Agents and Up to Nine Goods

We prove that every fair-division instance with four agents, additive valuations over the non-negative reals, and at most nine indivisible goods admits a \emph{complete} allocation that is envy-free up to any good in the strong, zero-tolerant sense ($\EFXo$). The case $m=9=n+5$ lies beyond the previously known frontier...