Prebidding first-price auctions with and without head starts

We study the effect of prebidding in first-price auctions with a single prize under incomplete information. The values of the n−1 bidders are private information while bidder 1's value is commonly known. Bidder 1 places his bid before all the n−1 bidders. We show that regardless of his value, bidder 1 always has a positive effect on the expected highest bid. However, bidder 1's contribution to the expected highest bid is not significant since the prebidding first-price auction with n bidders may be less profitable than the optimal simultaneous first-price auction with only n−1 bidders. On the other hand, by giving the optimal head start to bidder 1, the prebidding first-price auction is always more profitable than the optimal simultaneous first-price auction with n−1 bidders