Constrained School Choice

• Authors: Flip Klijn.
• BSE Working Paper: 109812 | September 15
• Keywords: stability , matching , acyclic priority structure , Nash equilibrium , school choice , Gale-Shapley deferred acceptance algorithm , top trading cycles , Boston mechanism , truncation
• JEL codes: C72, C78, D78, I20
• stability
• matching
• acyclic priority structure
• Nash equilibrium
• school choice
• Gale-Shapley deferred acceptance algorithm
• top trading cycles
• Boston mechanism
• truncation

Recently, several school districts in the US have adopted or consider adopting the Student-Optimal Stable mechanism or the Top Trading Cycles mechanism to assign children to public schools. There is evidence that for school districts that employ (variants of) the so-called Boston mechanism the transition would lead to efficiency gains. The first two mechanisms are strategy-proof, but in practice student assignment procedures typically impede a student to submit a preference list that contains all his acceptable schools. We study the preference revelation game where students can only declare up to a fixed number of schools to be acceptable. We focus on the stability and efficiency of the Nash equilibrium outcomes. Our main results identify rather stringent necessary and sufficient conditions on the priorities to guarantee stability or efficiency of either of the two mechanisms. This stands in sharp contrast with the Boston mechanism which has been abandoned in many US school districts but nevertheless yields stable Nash equilibrium outcomes.