Abstract

Two firms compete to attract and hire from a pool of workers of unknown productivity. Firms simultaneously post a selection procedure which consists of a test and an acceptance probability for each test outcome. After observing the firms' selection procedures, each worker can apply to one of them. Both firms have access to a limited set of feasible tests. The firms face two key considerations when choosing their selection procedure: the statistical properties of their test and the selection into the procedure by the workers. I identify two partial orders on tests that are useful to characterise the equilibrium of this game: the test's accuracy Lehmann (1988) and difficulty. I show that in any symmetric equilibrium of this game, the test chosen must be maximal in the accuracy order and minimal in the difficulty order. I use this result to show that when firms can flexibly design their test up to a cost constraint, the test used in a symmetric equilibrium exhausts the budget but the expected productivity at the high signal is zero. I also consider the cases where firms face capacity constraints or have the possibility of making a wage offer.