Optimality and Robustness of the English Auction
This paper attempts to reconcile the observed popularity of the English auction with the hypothesis that the trading mechanism is chosen with the objective of maximizing the seller's expected revenue. Under the assumptions of Milgrom and Weber's  'general symmetric model,' I show the following three results. First, the 'augumented' English auction, in which the auctioneer sets the reserve price after all but one bidder have dropped out, generates at least as much seller's expected revenue as any ex post incentive-compatible (EPIC) and individually rational (EPIR) direct mechanisms. EPIC and EPIR direct mechanisms correspond to "belief-free" selling procedures. Thus this restriction of the set of feasible selling mechanisms aims at capturing a notion of robustness with respect to pertubations of the buyers' beliefs about their opponents' private information. Second, in the larger set of mechanisms, characterized by the property that 'losers do not pay,' ther! e exist auctions that generate a higher seller's expected revenue than the (augmented) English auction. Third, with two buyers, for a large class of signals' distributions, the augmented English auction maximizes the seller's expected revenue among all selling procedures where the loser does not pay and each buyer's payment is nondecreaseing in his own signal. With private values, these two conditions are satisfied by many equilibria in a class of bidding mechanisms, which includes approximations of both the Dutch auction and the English auction with discrete price increments. With more than two buyers, the English auction is optmal among all ex post efficient mechanisms where the losers do not pay and each buyer's payment is monotone in his signal.
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