Score contribution per author:
α: calibrated so average coauthorship-adjusted count equals average raw count
We study multi-period college admission problems where, at each period, a matching is computed and students have the option to either finalize their matches or participate in the next period. Students participating in an additional run of the matching mechanism can submit a new rank order list to the matching clearinghouse. Such gradual matching systems can adequately account for an additional source of heterogeneity among participants, like withdrawals. We identify the conditions under which such systems first ensure that participating in additional runs of the matching mechanism is safe for participants (in the sense that they can secure the spot they obtained at the previous round) 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 end of the admission campaign.