Hidden Substitutes

Abstract

Substitutable preferences, i.e., preferences without complementarities, are necessary to guarantee the existence of stable outcomes in many market design settings. In this paper, we highlight a form of "hidden substitutability" that arises in many-to-one matching markets with contracts: some preferences over contracts that exhibit 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 contracting 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.