The paper extends envy-free allocation with subsidies to weighted entitlements, proving worst-case subsidy bounds and polynomial-time algorithms for monotone, superadditive, additive, binary, matroidal, and identical-item valuations.
We can modify Proposition 7.11 in the following way: for each agent i /∈ R(t), where t ∈ [T ], ℓi(X t)≤ 1 w2
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Whoever Said Money Won't Solve All Your Problems? Weighted Envy-free Allocation with Subsidy
The paper extends envy-free allocation with subsidies to weighted entitlements, proving worst-case subsidy bounds and polynomial-time algorithms for monotone, superadditive, additive, binary, matroidal, and identical-item valuations.