  We consider priority-based school choice problems with farsighted students.
We show that a singleton set consisting of the matching obtained from the Top
Trading Cycles (TTC) mechanism is a farsighted stable set. However, the
matching obtained from the Deferred Acceptance (DA) mechanism may not belong to
any farsighted stable set. Hence, the TTC mechanism provides an assignment that
is not only Pareto efficient but also farsightedly stable. Moreover, looking
forward three steps ahead is already sufficient for stabilizing the matching
obtained from the TTC.
