Generalized Second Price Auctions with Hierarchical Bidding

The sale of text advertisements on search engines using an auction format called Generalized Second Price (GSP) has become increasingly common. GSP is unique in that it allows bidders to revise their bid if they are unhappy with the result of the auction, and because the auction sells multiple units of a related good simultaneously. I model this sale as a hierarchical game with complete information, allowing one potential advertiser to bid in each stage. The hierarchical game has an entirely different set of equilibria from the simultaneous bid game studied in earlier research on this auction. Under hierarchical bidding, a Vickrey-Clarke-Groves setup guarantees higher auctioneer revenue than GSP.