Question: Consider the simple private-value auction with 6 bidders. Each bidder’s value is drawn independently from
(a) Suppose that the seller holds a second-price auction. What is the expected payoff of a bidder with value ∈ [4,10]?
(b) Suppose that the seller holds an auction with the following rules: the highest bidder wins the auction and pays the square of her bid (e.g., if bids are $6, $5, $4, $3, $2, $1, the payment is $36). Find an equilibrium bidding strategy. Edit
Answer: he generalized second-price auction (GSP) is a non-truthful auction mechanism for multiple items. Each bidder places a bid. The highest bidder gets the first slot, the second-highest, the second slot and so on, but the highest bidder pays the price bid by the second-highest bidder, the second-highest pays the price bid by the third-highest, and so on. First conceived as a natural extension of the Vickrey auction, it conserves some of the desirable properties of the Vickrey auction. It is used mainly in the context of keyword auctions, where sponsored search slots are sold on an auction basis. The first analyses of GSP arein the literature by Edelman, Ostrovsky, and Schwarz and by . It is used by Google's AdWords technology, and it was employed by Facebook, which has now switched to Vickrey–Clarke–Groves auction.
The generalized second-price auction (GSP) is a non-truthful auction mechanism for multiple items. Each bidder places a bid. The highest bidder gets the first slot, the second-highest, the second slot and so on, but the highest bidder pays the price bid by the second-highest bidder, the second-highest pays the price bid by the third-highest, and so on. First conceived as a natural extension of the Vickrey auction, it conserves some of the desirable properties of the Vickrey auction. It is used mainly in the context of keyword auctions, where sponsored search slots are sold on an auction basis. The first analyses of GSP are in the literature by Edelman, Ostrovsky, and Schwarz[1] and by . It is used by Google's AdWords technology, and it was employed by Facebook, which has now switched to Vickrey–Clarke–Groves auction Edit
