Stability and Matching with Aggregate Actors: A Perspective on Markets and Hierarchies

Many real-life problems involve the matching of talented individuals to institutions such as firms, hospitals, or schools, where these institutions are simply treated as individual agents. In this paper, I study many-to-one matching with contracts that incorporates a theory of choice of institutions, which are aggregate actors, composed of divisions that are enjoined by an institutional governance structure (or mechanism). Conflicts over contracts between divisions of an institution are resolved by the institutional governance structure, whereas conflicts between divisions across institutions are resolved, as is typically the case, by talents’ preferences. Noting that hierarchies are a common organizational structure in institutions, I offer an explanation of this fact as an application of the model, where stability is a prerequisite for the persistence of organizational structures. I show that stable market outcomes exist whenever institutional governance is hierarchical and divisions consider contracts to be bilaterally substitutable. In contrast, when governance in institutions is non-hierarchical, stable outcomes may not exist. Since market stability does not provide an impetus for reorganization, the persistence of markets with hierarchical institutions can thus be rationalized. Hierarchies in institutions also have the attractive incentive property that in a take-it-or-leave-it bargaining game with talents making offers to institutions, the choice problem for divisions is straightforward and realized market outcomes are pairwise stable, and stable when divisions have substitutable preferences.