Sticky matching in school choice

We introduce the notion of sticky-stability in order to accommodate appeal costs in real-life school-choice systems. When appealing is costly, students (or parents) may not find it worth appealing, even if their priorities are violated in their preferred schools. In order to incorporate this into the school-choice setting, we consider the vector of parameters, namely the profile of students’ stickiness degrees resulting from students’ cost-benefit analyses and consisting of each student’s least rank difference associated with appeals he/she finds beneficial. Then, sticky-stability rules out only appeal-causing priority violations. Consequently, we introduce the following two mechanisms, both of which elicit these parameters from students: “efficiency-improving deferred-acceptance mechanism” (EIDA) and “efficiency-corrected deferred-acceptance mechanism (ECDA). We show that both are sticky-stable and dominate stable matchings in terms of efficiency. Furthermore, the latter is efficient within the class of sticky-stable mechanisms. In a complete information setting, both are manipulable while the EIDA is immune to manipulations via stickiness degree misreporting. However, if students have limited information, then the EIDA becomes robust to manipulations, whereas the ECDA continues to be vulnerable, but with a diminished scope.