Combining Boston Mechanism with Deferred Acceptance Algorithm

We study the matching mechanism in a two-stage game that mixes two well-known matching mechanisms, Boston Mechanism(BM) and the Deferred Acceptance algorithm(DA). First, we show that if all organizations have the same preferences for agents they accept, the subgame perfect equilibrium outcome of the two-stage game is agent-optimal stable matching. We then show that at least one of the subgame perfect equilibria of the two-stage game is an agent-optimal stable matching if the condition of Ergin acyclicity is satisfied. Under a stronger version of Ergin acyclicity, we also show that DA outcome becomes weakly preferable for all agents to the two-stage game outcome