Albrecht, J., Cai, X., Gautier, P. and Vroman, S. (2020). Multiple applications, competing mechanisms, and market power Journal of Economic Theory, 190:1--39.

We consider a labor market with search frictions in which workers make multiple applications and firms can post and commit to general mechanisms that may be conditioned both on the number of applications received and on the number of offers received by the firm's candidate. When the contract space includes application fees, there exists a continuum of symmetric equilibria of which only one is efficient, and it has a posted wage equal to match output. In the inefficient equilibria, the wage is below match output, and the value of a worker's application depends on whether he or she receives another offer. This allows individual firms to free ride on one another and gives firms market power. When we endogenize the number of applications and allow for general mechanisms, only the efficient equilibrium survives. By allowing for general mechanisms, we are able to examine the sources of inefficiency in the multiple applications literature.