May 2021
Article
Review of Economic Studies

Stability, Strategy-Proofness, and Cumulative Offer Mechanisms

By: John William Hatfield, Scott Duke Kominers and Alexander Westkamp

Format:Print

Abstract

We consider the setting of many-to-one matching with contracts, where firms may demand multiple contracts, but each worker desires at most one contract. We introduce three novel conditions—observable substitutability, observable size monotonicity, and non-manipulatability—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, when the choice function of some firm fails any of our three conditions, one can construct unit-demand choice functions for the other firms such that no stable and strategy-proof mechanism exists. In the final part of the paper, we characterize the class of choice functions for which the cumulative offer mechanism is guaranteed to yield a stable outcome.

Keywords

Matching With Contracts; Stability; Strategy-proofness; Substitutability; Size Monotonicity; Cumulative Offer Mechanism; Marketplace Matching; Balance and Stability

Citation

Hatfield, John William, Scott Duke Kominers, and Alexander Westkamp. "Stability, Strategy-Proofness, and Cumulative Offer Mechanisms." Review of Economic Studies 88, no. 3 (May 2021): 1457–1502.