Envy-free, efficient and strategy-proof division of a heterogeneous good between two agents
The study examines dividing a resource [0,1] between two agents with ordinal preferences that are monotonic in quantity. It shows that a rule satisfying Pareto efficiency, envy-freeness, and strategy-proofness cannot exist. Fairness is determined by the agents' 'balanced cuts,' meaning no single rule can guarantee all three properties simultaneously.