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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 (legal) admissions preference schemes anddoi:10.2139/ssrn.2883307 fatcat:jm7h64mmofgr5noptt356b3nyy