Level-k reasoning in school choice

Boston Mechanism (BM) and Deferred Acceptance (DA) are two competing algorithms in school choice. BM is manipulable whereas DA encourages truth-telling. Recognizing heterogeneous sophistication of students, we use the level-k model to analyze students' strategies under BM in a complete information environment with strict school priorities. Because students tend to manipulate first choice under BM, we characterize the first choice reported by students at all possible sophistication levels. In a general framework we show that BM is no less efficient than DA, and in two specific belief settings we further show that it is as if students run DA in their minds when they make level-k reasoning under BM. We compare the relation between sophistication and welfare under BM in the two belief settings to emphasize the role of high sophistication and correct belief. We also compare our results with Nash equilibrium analysis.