Implementing matching rules by type pretension mechanisms

We consider a two-sided matching model where agents' preferences are a function of the types of their potential mates. Matching rules are manipulated by type misrepresentation. We explore the implementability of the G-core in G-Strong Nash Equilibria. Although direct type pretension mechanisms rule out “bad” equilibria, the existence of equilibrium cannot be generally guaranteed. However, taking G as the discrete partition, the individually rational matching correspondence is partially implementable in Nash equilibria. On the other hand, incorporating a certain degree of hypocrisy in the mechanism, i.e., allowing agents to pretend different types to different potential mates, ensures the full implementability of the G-core in G-Strong Nash Equilibria.