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Auction Theory

Auction TheoryJonathan LevinOctober 2004 Our next topic is auctions. Our objective will be to cover a few of themain ideas and highlights. Auction Theory can be approached from differentangles from the perspective of game Theory (auctions are bayesian gamesof incomplete information), contract or mechanism design Theory (auctionsare allocation mechanisms), market microstructure (auctions are models ofprice formation), as well as in the context of different applications (procure-ment, patent licensing, publicfinance, etc.). We re going to take a relativelygame-theoretic approach, but some of this richness should be The Independent Private Value (IPV) A ModelThe basic Auction environment consists of: Biddersi=1,..,n Oneobjecttobesold Bidderiobserves a signal Si F( ), with typical realizationsi [s,s], and assumeFis continuous. Bidders signalsS1,..,Snare independent.

1.2 Vickrey (Second-Price) Auction In a Vickrey, or second price, auction, bidders are asked to submit sealed bids b 1,...,bn. The bidder who submits the highest bid is awarded the object, and pays the amount of the second highest bid. Proposition 1 In a second price auction, it is a weakly dominant strategy to bid one’s value, bi(si)=si. Proof.

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