Manipulation of Attractiveness in Two-Sided Stable Matches

Most theoretical research on two-sided matching markets has focused on agents' incentives to misreport their own preferences while paying little attention to their incentives to manipulate the preferences of agents on the other side of the market. This paper attempts to fill this gap by showing that, in two-sided stable matching markets in which colleges are not fully allowed to express their true preferences over students, colleges have incentives to reduce their attractiveness among unacceptable students. We identify at least two conditions under which such behavior is expected to occur: when all colleges have the same ``legal preferences'' over students, or when the market is sufficiently large. This contrasts with previous results from the literature that would predict that colleges' incentives to reduce their quality for a subset of unacceptable students would disappear in large stable matching markets. Our results highlight the importance of the imposition of regulatory policies that not only prevent schools from giving low priority to less profitable students in the admission process, but also prevent them from discouraging the application of those students