Gradual College Admission

Abstract

We study multi-period college admission problems where, at each period, a matching is computed and students have option to either finalize their matches or participate to the next period. Students participating to an additional run of the matching mechanism can submit a new preference list to the matching clearinghouse. Such gradual matching systems can adequately account for an additional source of heterogeneity among participants, like scheduling constraints or withdrawals. We identify the conditions under which such systems first produce incentives to participate to additional runs of the matching mechanism and second yield to stable matchings (with a stability concept adapted to this environment). We use our results to evaluate the former French college admission system, where students could finalize their matches at different dates up to two months ahead the final date.

Pick-an-object Mechanisms

“…Other papers have also considered sequential versions of allocation rules, such as multiunit auctions (Ausubel, 2004(Ausubel, , 2006, stable (Bó and Hakimov, 2020;Kawase and Bando, 2019;Haeringer and Iehle, 2019) and more general allocations (Schummer and Velez, 2017). Moreover, there is a growing literature evaluating sequential mechanisms used in the field (Gong and Liang, 2016;Grenet et al, 2019;Veski et al, 2017;Dur et al, 2018).…”

Dynamically Stable Matching

“…Because my analysis is about a one-to-one matching market, the analysis in this paper has nothing in principle to say about the behavior of schools. 16 See, for instance, Westkamp (2013); Dur and Kesten (2014); Feigenbaum et al (2017); Dogan and Yenmez (2018); Haeringer and Iehlé (2019); Andersson et al (2018); Mai and Vazirani (2019). Except for the last two papers, this literature studies models that are in a sense static: the agents and their matching opportunities are fixed.…”