Verifiability and Group Formation in Markets

We consider group formation in markets with asymmetric information. Our model nests standard matching problems, including one-to-one, many-to-one, and many-to-many matching, as well as matching with salaries or contracts and matching with incomplete information. Prices for group positions and private goods as well as the groups that form are determined endogenously in equilibrium, as a result of demand and supply forces. The setup includes problems as diverse as moral hazard in teams, screening on ability, and mechanism design. Our analysis, including the definition of equilibrium and existence, revolves around the randomness in matching. Our main results characterize the limits on efficiency in such a general equilibrium, and show that a sufficiently rich set of group types can ensure the existence of an efficient equilibrium.