Deferred Acceptance with Clocked Skips in School Choice

We study the school-choice model of Abdulkadiroğlu and Sönmez (2003) with capped rank-order lists and introduce deferred acceptance with clocked skips (sDA). The mechanism combines DA-style tentative holding with a public round clock: a student who is displaced after being held resumes only at the current clock position and skips list positions that passed while she was held. We first show that every stable matching can be supported as a Nash-equilibrium outcome of the game induced by sDA. With cap one, sDA coincides with immediate acceptance, and its Nash-equilibrium outcomes are exactly the stable matchings. This exact implementation result continues to hold at cap two for every priority structure—a guarantee DA provides only under Ergin-acyclicity. With caps of three or more, however, unstable Nash-equilibrium outcomes can arise even in one-to-one markets; moreover, every Ergin-cycle can be used to support such an outcome for some preference profile. Surprisingly, equilibrium outcomes are not necessarily nested in the cap. These findings identify a niche for sDA in transparent short-list environments while cautioning that the cap is not a monotone design lever: longer lists can both create and destroy unstable equilibrium outcomes.