An "Alternating Recognition" Model of English Auctions
We attempt a more realistic abstraction of an English (oral ascending) auction than the standard, in Milgrom and Weber . In particular, the assumptions that exists are irrevocable and necessarily public are dropped. 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 exists. Such exits may be temporary, although we construct an equilibrium in which there is no benefit to exit and re-entry. 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. Hence, 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 the information less valuable. Consequently, the much simpler formula for expected revenue in second-price auctions may be the preferred approximation for English auctions.
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