An "Alternating Recognition" Model of English Auctions

We present an alternative abstraction of an English (oral ascending) auction to the standard, in Milgrom and Weber (1982), that accords more closely with practices in some auction markets. In particular, the assumptions that exits are irrevocable and necessarily public are dropped, making endogenous the decision to compete silently and privately, or openly. In the model, the price rises in a stylization of an auctioneer alternately recognizing two bidders who affirm willingness to pay the current price. The auctioneer pays attention to other bidders only when a recognized bidder exits. Such exits may be temporary, although we construct an equilibrium in which there is no benefit to exit and reentry. The number of public exits is stochastic; frequently a losing "bidder" will remain silent, giving no indication of his willingness to pay, and hence yielding no useful inference about his private information. Thus, the source of the expected revenue advantage of English auctions over second-price auctions is only stochastically available. Moreover, when public exits are incomplete, the ordinal rank of the bidder whose private information can be inferred is unknown, making that information less valuable. Consequently, the simpler formula for expected revenue in second-price auctions may be the preferred approximation for English auctions.