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In this study we present a simple mechanism in a many-to-one matching market where multiple costless applications are allowed. The mechanism is based on the principles of eligibility and priority and it implements the set of stable matchings in Subgame Perfect Nash Equilibrium. We extend the analysis to a symmetric mechanism where colleges and students interchange their roles. This mechanism also implements the set of stable matchings.

Non-Revelation Mechanisms in Many-to-One Markets