auction - AMS 335/ECO 355 Game Theory Chapter 2 Games of...

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AMS 335/ECO 355 Game Theory Fall 2010 Chapter 2 Games of Incomplete Information Zhen Xu 2.4 Auctions Page 1 of 5 The design and analysis of auctions is one of the triumphs of game theory. Auction theory was pioneered by the economist William Vickrey in 1961. Its practical use became apparent in the 1990s, when auctions of radio frequency spectrum for mobile telecommunication raised billions of dollars. Economic theorists advised governments on the design of these auctions, and companies on how to bid (see McMillan, “Selling spectrum rights,” Journal of Economic Perspectives Vol. 8, 1994, pages 145–162). The auctions for spectrum rights are complex. However, many principles for sound bidding can be illustrated by applying game-theoretic ideas to simple examples. This section highlights some of these examples; see Milgrom, “Auctions and bidding: a primer” ( Journal of Economic Perspectives Vol. 3, 1989, pages 3–22) for a broader view of the theory of bidding in auctions. Open Bid Auction The English Auction : the open ascending price auction. In one variant of the English auction, the sale is conducted by an auctioneer who begins by calling out a low price and raises it, typically in small increments, as long as there are at least two interested bidders. The auction stops when there is only one interested bidder. The Dutch Auction : the open descending price counterpart of the English auction. Here the auctioneer begins by calling out a price high enough so that presumably no bidder is interested in buying the object at that price. This price is gradually lowered until some bidder indicates her interest. The Sealed-Bid Auction : Bidders submit bids in sealed envelopes; the person submitting the highest bid wins the object. The Private Value Auction : Each bidder’s value derives from his personal information or tastes for the object, and not from other bidders’ information or considerations such as potential resale value. Eሾx ି୧ ሿൌEሾx The Common Value Auction: the object is worth the same to all bidders, bidders must decide how to take into account uncertainty about that value. In this case, each bidder may have, prior to the auction, received some private information or signals about the value of the object for sale. The Typical Model of Private Value Auctions There is a single indivisible object for sale and N potential buyers are bidding for the object. Bidder i ’s private value of the object is x i , which is the maximum amount he is willing to pay for the object, i.e. his bid b i x i . Each x i is independently and identically distributed on some interval [0, X] according to the distribution function F .
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AMS 335/ECO 355 Game Theory Fall 2010 Chapter 2 Games of Incomplete Information Zhen Xu 2.4 Auctions Page 2 of 5 Bidder i knows x i and only that other bidders' values are independently distributed according to F . Bidders are risk neutral - they seek to maximize their expected profits.
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This note was uploaded on 04/27/2011 for the course ECO 355 taught by Professor Xu during the Fall '10 term at SUNY Stony Brook.

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auction - AMS 335/ECO 355 Game Theory Chapter 2 Games of...

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