Fairness and Efficiency for Probabilistic Allocations with Endowments
summary
Proposes a concrete fairness rule called no justified envy that tolerates envy only when swapping would violate the other agent’s endowment, proves existence of fractional allocations that are Pareto‑optimal and individually rational under concave preferences, and shows Walrasian prices can fail (a 3‑agent counterexample with two objects). Tools: construction of price‑dependent income functions, utilitarian weight maximization and the KKM lemma (fixed‑point style). Results extend to convex policy constraints and expected‑utility domains.
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