On the existence of EFX allocations for goods

Key Points

• EFX allocations can always be achieved when two agents have arbitrary valuation functions, while others follow a specific pattern.
• The result applies to cases with multiple agents, establishing strong conditions for EFX allocation to hold.
• Approach involves theoretical proofs around valuation functions in diverse agent scenarios, focusing on monotonicity.
• Implications may guide future designs of fair allocation mechanisms in resource distribution with indivisible goods.