For any k>2, (k+1)/(k+2)-EFkX allocations exist for any number of agents and are polynomial-time computable; 3/4-EF2X holds for all agents and 2/3-EFX extends to 8 agents, while EFkX orientations are NP-complete to decide.
Proceedings of the 24th International Conference on Autonomous Agents and Multiagent Systems , pages =
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Approximate Envy-Free Allocations up to any $k$ Goods
For any k>2, (k+1)/(k+2)-EFkX allocations exist for any number of agents and are polynomial-time computable; 3/4-EF2X holds for all agents and 2/3-EFX extends to 8 agents, while EFkX orientations are NP-complete to decide.