Deposit Requirements in Auctions∗

We examine optimal auction design when buyers may receive future outside offers. The winning bidder may choose to default upon observing her outside offer. Under the optimal mechanism, the bidder with the highest value wins if and only if her value is above a cutoff, and the winner never defaults. The optimal auction takes the form of a second-price auction with a reserve price and a deposit by the winning bidder. Under regularity conditions, both the optimal reserve price and the deposit increase when the distribution of outside offers worsens.