Adverse selection in competitive search equilibrium

We extend the notion of competitive search equilibrium to an environment with adverse selection. Uninformed principals post contracts to attract informed agents. Agents observe the contracts and apply for one, trading off the probability of matching with a principal against the terms of trade offered by the contract. We characterize equilibria as the solution to a constrained optimization problem and show that in equilibrium principals offers separating contracts to attract different types of agents. We then present a set of examples to illustrate the usefulness of our model