A labor market with targeted wage offers

We model a market for highly skilled workers, such as the academic job market. The outputs of firm-worker matches are heterogeneous and common knowledge. Wage setting is synchronous with search: firms simultaneously make one personalized o¤er each to the worker of their choice. With large frictions (delay costs), efficient coordination is not possible, but for small frictions efficient matching with Diamond-type monopsony wages is an equilibrium.