Auctioneer’s Objective
So, we have four different rules, and we have predictions of their outcomes. Which one does the auctioneer choose?
The answer depends on the seller’s objective. If the auctioneer is a private entity, it is most likely trying to maximize its expected revenue from the sale. In that case, the auction rule under which it fetches the maximum revenue is the best rule for the auctioneer.
Of course, the auctioneer does not know the bidders’ values. So, the auctioneer then compares the rules by considering the expected revenues under the alternative rules. The expectation of revenue is based on the auctioneer’s beliefs about the unknowns of the auction. The unknowns of our simplified situation are the bidders’ values. We model the auctioneer as one who has a probability belief about the bidders’ values and calculates the expected revenues based on that belief.
The auctioneer may be interested in social efficiency. One way that economists calculate social efficiency is by calculating the “social surplus.” In the context of an auction, the social surplus is the sum of the consumption value generated as a result. For instance, if a bidder who has a value of $10 wins the object (and hence consumes it), the social surplus takes the value of $10. We say that one auction is more efficient than another if the former results in a larger social surplus than the latter. We say that an auction is efficient if there is no other auction rule that can generate a higher social surplus than this auction. Again, we compare auctions based on expected social surplus to figure out which is most efficient.
The auctioneer may also be a politician or a minister in a corrupt country, who neither cares about the revenue (to the government), nor the social efficiency. Instead, the minister or politician is interested in maximizing the bribe intake or some personal gain through some other means. The politician’s objective will be to find the auction that is most “manipulable” (least transparent to get away with corruption). The auction literature considers such objectives, too. But I will not talk about it here till I have finished writing about the other objectives.