This paper proposes a competition model in which universities freely fix their tuition fees in a setting where their soft capacity is chosen endogenously. Because of the growing competition between universities to attract additional students, universities choose to support an increasing marginal cost for students enrolled beyond their initial capacity. Our results show that i) a more convex cost leads the universities to choose a larger capacity but also higher tuition fees; ii) when the marginal cost is low, an increase in tuition fees with the number of universities is possible; iii) when the marginal cost is sufficiently high, competition between an increasing number of universities maintains fees at their maximum level (collusive fees) without reducing either the total number of admissions or social welfare.