Gautier, PieterA. and Holzner, ChristianL. (2017). Simultaneous search and efficiency of entry and search intensity American Economic Journal: Microeconomics, 9(3):245--282.

We consider a model where firms open vacancies and post and commit to a wage mechanism. Search is costly and workers simultaneously apply to multiple jobs. Firms can be connected to multiple workers and workers to multiple firms. We use a new method to derive the expected maximum number of matches in a large market as a function of the number of applications and market tightness. We also derive the conditions under which firm entry, worker participation, and search intensity are socially efficient. Finally, we show that a sequential auction under incomplete information can establish the social optimum and discuss some alternative mechanisms that can, under complete information of the entire network, also deliver social efficiency.