Efficient Investment, Search, and Sorting in Matching Markets

We study markets where heterogeneous agents first make investment decisions and then engage in costly search to form productive matches.The trading process is 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.