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THE THEORY OF FIRST-PRICE, SEALED-BID AUCTIONS

1. Within the class of first-price, sealed-bid auctions, there are a number of possible variations in environment, information, and rules: (1) The number of potential bidders is either known, or unknown with a distribution that is common knowledge. (2) There may be no reservation price, so that the item will definitely be sold, or there may be a reservation price which is announced or unannounced in advance of the auction. If there is a reservation price that is unannounced, then it may be made known after the auction is complete (e.g., as a losing bid), or the item may simply be withdrawn from the auction. If there are ties, there may be a tie-breaking mechanism, or subsequent rounds of bids between those tied. (3) The winning bid may be announced, or may be private information shared by the winner and seller, so that non-winners have only the (unverified) information that their bid was lower. Non-winning bids may be announced, or may be private information shared by a losing bidder and the seller. Finally, a third party acting as an agent for the seller and buyers may designate a winner (or announce the withdrawal of the item from the auction) without revealing the amounts of bids to either seller or buyers, or revealing the reservation price. Of course, if an item is sold, then the winning bid is known at least to the buyer and seller. These information differences are not germane in a " one-shot " auction, but are relevant if there is a possibility of resale or re-auction. (4) There may or may not be an opportunity for negotiation after the auction. One alternative is that bids are binding. Another is that they may contain contingencies whose value and prospects for clearing offer players the opportunity for post-auction negotiation. If such contingencies are allowed, then there must be a mechanism for terminating negotiations with the winning bidder if the contingencies are not satisfied, and negotiating with a lower bidder or restarting the auction. An obvious consequence of allowing contingencies in bids is that setting contingencies becomes part of the bidder's strategy, where a high bid with contingencies offers the opportunity to engage in bilateral negotiations with less effective competition from potential rival buyers. Finally, if one player (not necessarily a bidder) has a right of first refusal (RFR), then all bidders must take into account the possibility that this …