Price formation in a matching market with targeted offers

•We model a matching market with two-sided vertical differentiation.•Prices are determined by targeted offers made from one side.•When players are patient the matching that results in equilibrium is efficient, with the offerors taking all the surplus.•Otherwise, mixed strategies are used resulting in mismatch and delay.

We model a market where the surpluses from seller-buyer matches are heterogeneous but common knowledge. Price setting is synchronous with search: buyers simultaneously make one personalized offer each to the seller of their choice. With impatient players efficient coordination is not possible, and both temporary and permanent mismatches occur. Nonetheless, for patient players efficient matching (with monopsony wages) is an equilibrium. The setting is inspired by a labor market for highly skilled workers, such as the academic job market, but it can be easily adapted to, for example, the housing market or Internet advertising auctions.