College assignment as a large contest

We develop a model of college assignment as a large contest wherein students with heterogeneous learning-costs compete for seats at vertically differentiated colleges through the acquisition of productive human capital. We use a continuum model to approximate the outcomes of a game with large, but finite, sets of colleges and students. The continuum approximation lends tractability to a rich model for studying investment incentives in rank-order competitions. By incorporating two common families of affirmative action mechanisms into our model, admissions preferences and quotas, we can show that (legal) admissions preference schemes and (illegal) quotas have the same sets of equilibria including identical outcomes and investment strategies.