Auction Theory Stanford University（拍卖理论斯坦福大学）.pdfVIP

Auction Theory Jonathan Levin October 2004 Our next topic is auctions. Our objective will be to cover a few of the main ideas and highlights. Auction theory can be approached from different angles – from the perspective of game theory (auctions are bayesian games of incomplete information), contract or mechanism design theory (auctions are allocation mechanisms), market microstructure (auctions are models of price formation), as well as in the context of different applications (procure- ment, patent licensing, public finance, etc.). We’re going to take a relatively game-theoretic approach, but some of this richness should be evident. 1 The Independent Private Value (IPV) Model 1.1 A Model The basic auction environment consists of: • Bidders i= 1,...,n • One object to be sold • Bidder i observes a “signal” Si ∼ F(·), with typical realization s ∈i [s,s], and assume F is continuous. • Bidders’ signals S ,...,S are independent. 1 n • Bidder i’s value v (s) = s . i i i Given this basic set-up, specifying a set of auction rules will give rise to a game between the bidders. Before going on, observe two features of the model that turn out to be important. First, bidder i’s information (her signal) is independent of bidder j’s information. Second, bidder i’s value is independent of bidder j’s information – so bidder j’s information is private in the sense that it doesn’t affect anyone else’s valuation. 1 1.2 Vickrey (Second-Price) Auction In a Vickrey, or second price, auction, bidders are asked to submit sealed bids b ,...,b . The bidder who submits the highest bid is awarded the object, 1 n and pays the amount of the seco