Menu mechanisms

We investigate menu mechanisms: dynamic mechanisms where at each history, an agent selects from a menu of his possible assignments. We consider both ex-post implementation and full implementation, for both subgame perfection and a strengthening of dominance that covers off-path histories, and provide conditions under which menu mechanisms provide these implementations of rules. In comparison to direct mechanisms, menu mechanisms offer better privacy to participants; we formalize this with a novel notion of mechanism informativeness. Our results cover a variety of environments, including elections, marriage, college admissions, auctions, labor markets, matching with contracts, and object allocation.