Full Extraction of the Surplus in Bayesian and Dominant Strategy Auctions

Abstract

We consider auctions for a single indivisible object, in the case where the bidders have information about each other which is not available to the seller. We show that the seller can use this information to his own benefit, and we completely characterize the environ- ments in which a well chosen auction gives him the same expected payoff as that obtainable were he able to sell the object with full information about each bidder's willingness to pay. We provide this characterization for auctions in which the bidders have dominant strate- gies, and for those where the relevant equilibrium concept is Bayesian Nash. In both set-ups, the existence of these auctions hinges on the possibility of constructing lotteries with the correct properties. WE CONSIDER the situation in which an agent, the seller, possesses one indivisible unit of a good to which he attaches no value. But the good has value to a number of potential buyers, and its transfer to one of them would increase social welfare. In particular, the transfer to the buyer with the highest valuation maximizes social welfare. In this paper, we completely characterize environments in which the seller can design an auction that will enable him to capture for himself the full increase in social welfare induced by the transfer of the good to the bidder with the highest willingness to pay. If the seller had full information about the reservation prices of potential buyers, his optimal selling strategy would be very simple. He would announce a price equal or very close to the highest reservation value. The optimal strategy for the bidder with the highest evaluation would be to accept the offer. (Note that we are treating a situation in which the seller can commit himself to a price.) As a result of the exchange, the utility of the seller increases by the full amount of the increase in social welfare, and he has been able to fully extract the surplus. In many circumstances, however, a seller has only imperfect knowledge of the buyers' willingnesses to pay. In this case, he must find some mechanism, or auction, which will enable him to maximize his benefit from the sale of the object. The auction literature starts with this observation and shows how the seller can, by an astute choice of auction, extract the largest possible fraction of the surplus. In general, the literature has shown that this proportion is strictly less than one. In some circumstances, the bidders will have information about each other which is not available to the seller. For instance, in auctions for petroleum drilling rights, bidders know the results of geological tests which they have