  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.
