Hiring procedures to implement stable allocations

We implement the core correspondence in Subgame Perfect Equilibrium using a simple sequential mechanism in which firms propose a salary to each worker (in the first stage). Then , each worker accepts at most one proposal (second stage). Moreover, we show that, if agents' preferences are additive, this mechanism implements in Subgame Perfect Equilibrium that firms' optimal correspondence when firms employ undominated strategies. Finally we construct another simple sequential mechanism to implement workers' optimal correspondence when agents' preferences are additive