We prove the existence of a pure strategy Nash equilibrium for a finite directed search economy with heterogeneous firms, homogeneous workers and a general production technology. We use this result to provide a new characterization of the equilibrium set for the finite economy. We also show that, as the number of agents increases, the equilibria of the finite economy converge to the equilibria of competitive search economies with a continuum of agents; therefore, competitive search models have solid microfoundations.