The Affiliate Matching Problem: On Labor Markets where Firms are Also Interested in the Placement of Previous Workers
This addresses labor market inefficiencies for firms like consulting agencies and universities, but it is incremental as it builds on existing matching theory with new preferences.
The paper tackles the affiliate matching problem in labor markets where firms care about both hiring new workers and placing their own affiliated workers at other firms, modeling it as a generalization of the stable marriage problem. They found through a human survey that participants' preferences for affiliate workers violate classical assumptions, leading to nuanced stability definitions and an example marketplace that is stable under one definition but not another.
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.