This paper analyzes simple mechanisms implementing (subselections of) the core correspondence of matching markets. We provide a sequential mechanism which mimics a matching procedure for many-to-one real life matching markets. We show that only core allocations should be attained when agents act strategically when faced with this mechanism. We also provide a second mechanism to implement the core correspondence in Subgame Perfect Equilibrium.Alcalde’s work is partially supported by the Institut Valencia d’Investigacions Econòmiques and DGICYT under project PB 97–0131. Romero–Medina acknowledges financial support from the Instituto de Estudios Fiscales and DGICYT under project PB 92–0590.Publicad