Many public school choice programs use centralized mechanisms to match
 students with schools in the absence of market-clearing prices. Among
 them, the Boston mechanism is one of the most widely used. It is
 well-known that truth-telling may not be optimal under the Boston
 mechanism, which raises the concern that the mechanism may create a
 disadvantage to parents who do not strategize or do not strategize
 well. Using a data set from Beijing, this paper investigates parents’
 strategic behaviors under the Boston mechanism and its welfare
 implications. School choice is modeled as a simultaneous game with
 parents’ preferences being private information. The paper derives
 restrictions on parents’ behavior under various assumptions on their
 sophistication, or ability to predict others’ behavior, and the model
 is estimated using simulated maximum likelihood. The results suggest
 that parents’ sophistication is heterogeneous; when parents have a
 greater incentive to behave strategically, they pay more attention to
 uncertainty and strategize better. There is also evidence, although
 not robust, that wealthier and/or more educated parents strategize
 worse. If the Boston mechanism is replaced by the Deferred-Acceptance
 mechanism under which truth-telling is always optimal, the majority of
 the sophisticated parents who always play a best response are worse
 off. The reform benefits about half of the naive parents who are
 always truth-telling under the Boston mechanism, while it also hurts a
 non-negligible portion of them.