Hidden Substitutes

By: John William Hatfield and Scott Duke Kominers

Format:Print
| Language:English

Abstract

In this paper, we show that preferences exhibiting some forms of complementarity in fact have an underlying substitutable structure. Specifically, we show that some preferences that are not substitutable in the setting of many-to-one matching with contracts become substitutable when an employer is allowed to sign multiple contracts with an individual worker. These substitutably completable preferences guarantee the existence of stable outcomes, even though stable outcomes are not guaranteed, in general, when complementarities are present. Our results imply the existence of a stable, strategy-proof mechanism for allocating workers with specialized skillsets; moreover, our results give new insight into the existing applications of matching with contracts to cadet–branch matching and the design of affirmative action programs.