This note investigates the impact of application fees on student strategies within the

Deferred Acceptance mechanism (DA). We demonstrate that application fees reduce the

set of Nash equilibria under DA. While this reduction may preserve the existence of Nash

equilibria leading to assignments Pareto-dominating the student-optimal stable assignment,

it may also preclude the existence of such equilibria. This occurs when application fees are

positive for all students at a given school.

JEL Classification: C78, D47, D82.

Keywords: Matching; Application fees; Efficiency; Deferred acceptance; Nash Equilibrium