“Optimal Auction Design”, 1981-02 ():
This paper considers the problem faced by a seller who has a single object to sell to one of several possible buyers, when the seller has imperfect information about how much the buyers might be willing to pay for the object. The seller’s problem is to design an auction game which has a Nash equilibrium giving him the highest possible expected utility.
Optimal auctions are derived in this paper for a wide class of auction design problems.
…The general plan of this paper is as follows. §2 presents the basic assumptions and notation needed to describe the class of auction design problems which we will study. In §3, we characterize the set of feasible auction mechanisms and show how to formulate the auction design problem as a mathematical optimization problem. Two lemmas, needed to analyze and solve the auction design problem, are presented in §4. §5 describes a class of optimal auctions for auction design problems satisfying a regulatory condition. This solution is then extended to the general case in §6. In §7, an example is presented to show the kinds of counter-intuitive auctions which may be optimal when bidders’ value estimates are not stochastically independent. A few concluding comments about implementation are put forth in §8.
[Vitalik Buterin discussing domain name auction mechanism design:]
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