Fair Division

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 bun...

What is the best α for which α-MMS (maximin share) allocations always exist? The maximin share (MMS) is the value an agent can guarantee by dividing items into n bundles and receiving the worst bun...