The Assignment of Workers to Jobs In an Economy with Coordination Frictions

This paper studies the assignment of heterogeneous workers to heterogeneous jobs in the presence of coordination frictions. Firms offer human-capital-contingent wages, workers observe these and apply for a job. In a symmetric equilibrium, identical workers use identical mixed strategies in deciding where to apply, and the randomness introduced by mixed strategies generates equilibrium unemployment and vacancies. The equilibrium can be interpreted as the competitive equilibrium of a closely related model, ensuring constrained efficiency. The model generates a rich interaction between the heterogeneous workers and firms. Firms attract applications from multiple types of workers, and earn higher profits when they hire a more productive worker. Identical workers apply for jobs with different productivity and get higher wages when they land a more productive job. Despite this mismatch, I show that in some special cases, the model generates assortative matching, with a positive correlation between matched workers' and firms' productivity.