Strategic Disaggregation in Matching Markets

What happens after agents match can lead to strategic behavior that is often overlooked in matching theory. We demonstrate the linkage between pre- and post-match actions by introducing a game in which universities can force students to commit to majors before matriculating or to allow students to pick their majors during their studies. The interaction between "matching forces" (competition for higher quality partners) and "principal-agent forces" (moral hazard and adverse selection) leads to two different equilibria mirroring the American and English admissions systems.With monetary transfers, our model provides new insight into whether student athletes should be paid. Price competition removes the surplus to enrolling top students, making it impossible to sustain the American admissions equilibrium without an exogenous transfer cap. We show that properly designed transfer caps can achieve the first-best welfare outcome, and can lead to Pareto improvements over the status quo.