A mediator is a reliable entity which plays on behalf of the players who give her the right to play. The mediator acts in a pre-specified way based on messages received from the players. However, a mediator cannot enforce behavior; that is, players can play in the game directly without the...

We study many-to-one matching markets where hospitals have responsive preferences over students. We study the game induced by the student-optimal stable matching mechanism. We assume that students play their weakly dominant strategy of truth-telling.