Stability, Strategy-Proofness, and Cumulative Offer Mechanisms

John William Hatfield; Scott Duke Kominers; Alexander  Westkamp

Article | Review of Economic Studies | Forthcoming

Stability, Strategy-Proofness, and Cumulative Offer Mechanisms

by John William Hatfield, Scott Duke Kominers and Alexander Westkamp

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;

Format: Print

Read Now

Citation:

Hatfield, John William, Scott Duke Kominers, and Alexander Westkamp. "Stability, Strategy-Proofness, and Cumulative Offer Mechanisms." Review of Economic Studies (forthcoming).

COVID-19 convalescent plasma (CCP) therapy is currently a leading treatment for COVID-19. At present, there is a shortage of CCP relative to demand. We develop and analyze a model of centralized CCP allocation that incorporates both donation and distribution. In order to increase CCP supply, we introduce a mechanism that utilizes two incentive schemes, respectively based on principles of “paying it backward" and “paying it forward." Under the first scheme, CCP donors obtain treatment vouchers that can be transferred to patients of their choosing. Under the latter scheme, patients obtain priority for CCP therapy in exchange for a future pledge to donate CCP if possible. We show that in steady-state, both principles generally increase overall treatment rates for all patients—not just those who are voucher-prioritized or pledged to donate. Our results also hold under certain conditions if a fraction of CCP is reserved for patients who participate in clinical trials. Finally, we examine the implications of pooling blood types on the efficiency and equity of CCP distribution.

We prove configuration results for extremal Type II codes, analogous to the configuration results of Ozeki and of the second author for extremal Type II lattices. Specifically, we show that for n ∈{8,24,32,48,56,72,96} every extremal Type II code of length n is generated by its codewords of minimal weight. Where Ozeki and Kominers used spherical harmonics and weighted theta functions, we use discrete harmonic polynomials and harmonic weight enumerators. Along the way we introduce "t12-designs" as a discrete analog of Venkov's spherical designs of the same name.

Faculty & Research

Stability, Strategy-Proofness, and Cumulative Offer Mechanisms

Abstract

Citation:

About the Author

More from the Author