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
A Vickrey auction or sealed-bid second-price auction (SBSPA) is a type of sealed-bid auction. Bidders submit written bids without knowing the bid of the other people in the auction. The highest bidder wins but the price paid is the second-highest ...
, 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
economics
Economics () is the social science that studies the production, distribution, and consumption of goods and services.
Economics focuses on the behaviour and interactions of economic agents and how economies work. Microeconomics analyzes ...
literature by Edelman, Ostrovsky, and
Schwarz[Benjamin Edelman, Michael Ostrovsky, and Michael Schwarz:]
Internet Advertising and the Generalized Second-Price Auction: Selling Billions of Dollars Worth of Keywords
. American Economic Review 97(1), 2007 pp 242-259 and by
Varian.
[H. R. Varian:]
Position auctions. International Journal of Industrial Organization, 2006
. It is used by Google's
AdWords
Google Ads (formerly Google AdWords) is an online advertising platform developed by Google, where advertisers bid to display brief advertisements, service offerings, product listings, or videos to web users. It can place ads both in the result ...
technology, and it was employed by Facebook, which has now switched to
Vickrey–Clarke–Groves auction
A Vickrey–Clarke–Groves (VCG) auction is a type of sealed-bid auction of multiple items. Bidders submit bids that report their valuations for the items, without knowing the bids of the other bidders. The auction system assigns the items in a ...
.
Formal model
Suppose that there are
bidders and
slots. Each slot has a probability of being clicked of
. We can assume that top slots have a larger probability of being clicked, so:
:
We can think of
additional virtual slots with click-through-rate zero, so,
for