Dominant strategy implementation of stable rules

Most priority-based assignment problems are solved using the deferred acceptance algorithm. Kojima (2010) shows that stability and nonbossiness are incompatible. We show that the deferred acceptance algorithm satisfies a weaker notion of nonbossiness for every substitutable priority structure. We also discuss the multiplicity of dominant strategy equilibria of the preference revelation game induced by the deferred acceptance algorithm. We show that even untruthful dominant strategy equilibria lead to the truthful equilibrium outcome. In other words, the deferred acceptance algorithm is dominant strategy implementable.