The Review of Methods for Assignment of Elective Courses at Universities

In this paper we present a review of matching algorithms that are used for matching students with elective courses at universities. This is an example of a market where price mechanism cannot be used to determine the equilibrium allocation. In the Random Serial Dictatorship students select courses based on their position in a random queue. This mechanism is not ex post Pareto-efficient and its drawback is overcome in the Probabilistic Serial Assignment, although this mechanism is not strategy-proof. In the auction mechanism, students’ bids for courses do not represent their true preferences, since bids depend on their beliefs about the popularity of courses. The efficient allocation is obtained when Deferred Acceptance Algorithm is used - where the priority of students is determined based on their bids. Harvard draft mechanism is based on changing the order of students in the random queue from one round to another and this mechanism is not strategy-proof; however, it is, by all means, better for students than Random Serial Dictatorship. The Wharton Business School mechanism is based on the calculation of approximate competitive equilibrium.