_The Optimality of Being Efficient_ _3_ constrained optimal auction program. Thus, an equilibrium of the two-stage game cannot result in greater revenues.

We next consider whether misassigmnent actually hurts the seller. Does the seller necessarily get strictly lower revenues by any misassignment of the good? We show that the answer is yes in the identical objects model. The seller does strictly better by assigning the goods to those with the highest values. Intuitively, misassigning the goods results in the seller foregoing a share of the gains from trade that are ultimately captured by the bidders in resale.

Finally, we explore how a seller can implement optimal auctions with resale. We prove in a private-value setting that the Vickrey auction is not distorted by resale. When the seller uses a Vickrey - - auction, sincere bidding followed by no resale is an equilibrium in the auction-plus-resale game. Thus, a Vlickrey auction implements the efficiency-constrained optimal auction, if the lowest bidder types get a payoff of _0.2_ Our results thus provide a new defense for emphasizing _efficient_ auction design rather than _optimal_ auction design.<sup>3</sup> The presence of a perfect resale market forces even the most selfish seller, - - whose sole objective is maximizing revenues, to focus out of necessity on efficiency. While the Coasean assumption of _perfect resale_ is extreme, it is no more extreme than the standard assumption of _no resale_ which the auction literature routinely makes.

- In this paper, we focus solely on the Coasean critiques of the unconstrained optimal auction. Other available critiques strengthen our conclusion. For example, when one recognizes that bidder participation is affected by the auction design, then the case for an efficient auction improves. McAfee and McMillan (1987), Harstad (1990, 1993), and Levin and Smith (1994, 1995, 1996) provide justification why a revenue-maximizing seller should care about efficiency. With endogenous bidder participation and symmetric bidders, efficiency and revenue-maximization are equivalent. Bulow and Klemperer (1996) demonstrate that if a reserve price discourages even a single potential bidder from participating, the reserve makes the seller worse off.

Amother critique of the optimal auction approach is the severe informational requirement placed on the mechanism designer. The approach assumes that the distributions of private information are commor nknowledge, and the optimal auction makes explicit use of this information. If the seller does not know the distributions or is constrained to adopt auction rules that are independent of the distributions, then implementing the optimal auction may be impossible (but see Caillaud and Robert, 1998). In contrast, the informnational requirements of the efficient auction are often less severe. In interesting cases, the efficient auction rules may be independent of the distributions of private information (see, for example, Ausubel, 1997).

Our paper, by introducing a resale constraint into the optimal auction, is connected to both the resale lite:rature and the optimal auction literature. The study of resale in auction markets is just emerging. Bikhchandani and Huang (1989) and Viswanathan and Wang (1996) develop a model of

**_2_** Krishna and Perry (1997) show that in a market without resale the Vickrey auction implements the efficiencyconstrained[ optimal auction, when the lowest types get 0.

_3_ Recent papers emphasizing efficiency rather than revenue maximization as the seller's objective include Ausubel (1997), Ausubel and Cramton (1998), Dasgupta and Maskin (1997), and Krishna and Perry (1997). The real-world discussion of how best to structure the FCC spectrum auctions tended also to emphasize efficiency over revenue maxrimization.