Asymmetric Sequential Search under Incomplete Information

We study a two-stage sequential search model with two agents who compete for one job. The agents arrive sequentially, each one in a different stage. The agents' abilities are private information and they are derived from heterogeneous distribution functions. In each stage the designer chooses an ability threshold. If an agent has a higher ability than the ability threshold in the stage in which he arrives, he gets the job and the search is over. We analyze the equilibrium ability thresholds imposed by the designer who wishes to maximize the ability of the agent who gets the job minus the search cost. We also investigate the ratio of the equilibrium ability thresholds as well as the optimal allocation of agents in both stages according to the agents' distributions of abilities.