Who Gets What - And Why: The Hidden World of Matchmaking and Market Design

by Alvin E. Roth

Step 0. Applicants and employers privately submit preferences to a clearinghouse in the form of rank order lists. Step 1. Each employer offers jobs to its top-choice candidates, up to the number of its available positions. Each applicant looks at all the offers he or she has received, tentatively accepts the best one (the one highest on her preference list), and rejects any others (including any offers of jobs that were judged unacceptable and left off the applicant’s rank order list). … Step n. Each employer that had a job offer rejected in the previous step offers that job to its next choice, if one remains. Each applicant considers the offer he or she has been holding together with his or her new offer(s) and tentatively accepts the most preferred (highest-ranked) of these. The applicant rejects any remaining offers — including possibly the one that had been tentatively accepted earlier but is no longer the best offer received. (Note that applicants take no account of the step of the algorithm in which an offer was received; they look only at whether they prefer it to their other offers.) The algorithm ends when no offer is rejected, so that no firm wants to make any additional offers. At that point, each applicant and employer is (finally) matched by having each applicant accept whatever offer he or she had most recently tentatively accepted. That is, all acceptances are deferred until the end, when no more offers are forthcoming.

Deferred Acceptance Algorithm