Empirical and experimental evidence suggests different levels of sophistication among families in the Boston Public School student assignment plan. We analyze the preference revelation game induced by the Boston mechanism with sincere players who report their true preferences and sophisticated players who play a best response. We characterize the set of Nash equilibrium outcomes as the set of stable matchings of a modified economy, where sincere students lose priority to sophisticated students. Any sophisticated student weakly prefers her assignment under the Pareto-dominant Nash equilibrium of the Boston mechanism to her assignment under the recently adopted student-optimal stable mechanism. (JEL D82, I21)
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