# Hybrid mechanisms for Vickrey–Clarke–Groves and generalized second-price bids

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## Abstract

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.

## Keywords

Hybrid mechanisms Vickrey–Clarke–Groves Generalized second-price Position auctions Online advertising## JEL Classification

D44 D47## Notes

### Acknowledgements

I thank Gagan Aggarwal, Joshua Dillon, Chris Harris, Tim Lipus, Preston McAfee, Prabhakar Raghavan, Michael Schwarz, Mukund Sundararajan, Hal Varian, the anonymous associate editor, and the anonymous referee for helpful comments and discussions.

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