College Assignment as a Large Contest

We develop a model of college assignment as a large contest wherein students with heterogeneous abilities 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. By incorporating two common forms of affirmative action in our model, admissions preferences and quotas, we can show that admissions preference schemes and quotas are equivalent with respect to both college placement outcomes as well as induced incentives for human capital investment. Outcome equivalence may pose challenges for existing legal precedent which holds that admission preferences are legal whereas quotas are illegal based on supposed differences in how these systems achieve their intended goal. Finally, we assess the welfare costs of using human capital accumulation to compete for college admissions. While competition is necessary for an assortative (and welfare enhancing) match, the welfare losses from the accumulation of human capital solely to compete for a better college seat are also significant.