Competitive markets with private information on both sides

We consider competitive markets with asymmetric information. We define a notion of equilibrium that allows individuals to act strategically both as buyers and as sellers. In an example, the wage is common to all types of labor, and it does not reveal information concerning the skill levels of workers. However, at the solution we propose, an informed firm can take advantage of its superior information: it can choose the extent to which it concentrates its employment offers to workers of different types. The probabilities that offers to workers of different types produce a hire are treated parametrically by firms who have correct expectations about them, and firms forego the wage when they extend an offer whether the offer is successful or not. In a general framework, we prove that equilibria exist.