Stability, Strategy-Proofness, and Cumulative Offer Mechanisms

We characterize when a stable and strategy-proof mechanism is guaranteed to exist in the setting of many-to-one matching with contracts. We introduce three novel conditions—observable substitutability, observable size monotonicity, and non-manipulability via contractual terms—and show that when these conditions are satisfied, the cumulative offer mechanism is the unique mechanism that is stable and strategy-proof (for workers). Moreover, we show that our three conditions are, in a sense, necessary: If the choice function of some firm fails any of our three conditions, we can construct unit-demand choice functions for the other firms such that no stable and strategy-proof mechanism exists. Thus, our results provide a rationale for the ubiquity of cumulative offer mechanisms in practice.

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