The Affiliate Matching Problem: On Labor Markets where Firms are Also Interested in the Placement of Previous Workers

TL;DR

This paper introduces a generalized affiliate matching model in labor markets, exploring how firms' preferences over their own affiliates influence stable matchings and proposing a research agenda for centralized matching mechanisms.

Contribution

It extends the classic stable marriage model to include preferences over affiliates' matches, supported by survey data and stability analysis under different definitions.

Findings

Participants prefer their own affiliates in unexpected ways

Different stability definitions lead to different match outcomes

A marketplace example shows varying stability results

Abstract

In many labor markets, workers and firms are connected via affiliative relationships. A management consulting firm wishes to both accept the best new workers but also place its current affiliated workers at strong firms. Similarly, a research university wishes to hire strong job market candidates while also placing its own candidates at strong peer universities. We model this affiliate matching problem in a generalization of the classic stable marriage setting by permitting firms to state preferences over not just which workers to whom they are matched, but also to which firms their affiliated workers are matched. Based on results from a human survey, we find that participants (acting as firms) give preference to their own affiliate workers in surprising ways that violate some assumptions of the classical stable marriage problem. This motivates a nuanced discussion of how stability could be defined in affiliate matching problems; we give an example of a marketplace which admits a stable match under one natural definition of stability, and does not for that same marketplace under a different, but still natural, definition. We conclude by setting a research agenda toward the creation of a centralized clearing mechanism in this general setting.