Optimal Search Auctions with a Deadline

How to search for potential bidders to allocate a product by a deadline? We fully solve the optimal mechanisms, which can be implemented by a sequence of second-price auctions with properly selected reserve prices and sampling rules. The optimal search for long-lived bidders is characterized by a constant reserve (except for the last period) and contingent sample sizes, and that for short-lived bidders is by decreasing reserves and increasing sample sizes over time. Moreover, a seller with short-lived bidders searches more intensively and accepts lower reserve prices for stopping. We also solve the efficient mechanisms and provide relevant comparative results.