First–Price Auctions, Seller Information and Commitment to Sell

I consider an independent private values auction environment with risk–neutral buyers and an either risk–neutral or risk–averse seller. My setting differs from standard settings in two respects. First, the seller does not know his reservation value at the time he designs the auction, and second, he cannot commit to selling after observing the outcome of the auction. For general distributions of buyer types, I show that it might be optimal for a risk–neutral seller who wants to use an auction with a first–price payment rule to prohibit intermediate bids in addition to setting a reserve price. Moreover, if the seller is risk–averse instead of risk–neutral, choosing a first–price auction with a non–connected set of admissible bids while still uninformed might be strictly optimal for the seller, even if he can wait until he learns his reservation value and design the auction then.