In the college admission problem, we show that the student-optimal stable matching is weakly Pareto optimal for students if colleges' preferences satisfy substitutability and the law of aggregate demand. We also show that both of these properties are important for the result.

Stability is a central concept in matching theory, while nonbossiness is important in many allocation problems. We show that these properties are incompatible: there does not exist a matching mechanism that is both stable and nonbossy.