An allocation procedure using a fixed priority order: each participant in turn selects one remaining object, which is permanently assigned to them. For participants whose utilities depend only on their own assigned objects, strict rankings give a unique best available choice and the resulting allocation is Pareto optimal. If a proposed Pareto improvement changes an assignment, its earliest changed participant loses their unique best available object. With ties or allocation externalities, that argument requires additional assumptions.
[ref]
One-sided matchings: house allocation problems in the Cornell networks and markets text. §13.2, serial dictator mechanism and Theorem 13.2
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