Equilibrium directed search with multiple applications

We analyse a model of equilibrium directed search in a large labour market. Each worker, observing the wages posted at all vacancies, makes a fixed, finite number of applications, a. We allow for the possibility of ex post competition should more than one vacancy want to hire the same worker. For each a, there is a unique symmetric equilibrium in which all vacancies post the same wage. When a = 1, the common posted wage lies between the competitive and monopsony levels, and equilibrium is efficient. When a > 1, all vacancies post the monopsony wage. Some workers fail to find a job, some find a job at the monopsony wage, and some-those for whom there is competition-get the competitive wage. Equilibrium is inefficient when a > 1; in particular, there is excessive vacancy creation.