Hybrid Mechanisms for Vickrey-Clarke-Groves and Generalized Second-Price Bids

This paper analyzes mechanisms for selling advertising opportunities for several different positions on a page that would enable some advertisers to bid using Vickrey-Clarke-Groves (VCG) pricing while other advertisers bid using generalized second-price (GSP) pricing. I focus on a setting in which the number of ads displayed may vary with the advertisers’ bids and showing fewer ads enables the remaining ads to obtain more clicks. I illustrate the types of mechanisms one can construct that would ensure that VCG bidders have an incentive to bid truthfully, GSP bidders cannot obtain the same number of clicks at a lower price by varying their bid, and if all bidders bid using VCG (GSP) pricing, then the outcome is the same as it would be under the VCG (GSP) mechanism.