Efficient investment, search, and sorting in matching markets

We study markets where heterogeneous agents first make investment decisions and then engage in a costly search to form productive matches. The trading process is a random search and bargaining with explicit search costs. Despite potential hold‐up and matching problems, we prove that the constrained efficient allocation is an equilibrium: the agents' private incentives to invest and to accept/reject potential partners as they search are perfectly aligned with the social benefit. Furthermore, we establish a new sorting result for two‐sided markets, equilibrium existence, and conditions for uniqueness.