Hybrid advertising auctions

Facebook and Google offer hybrid advertising auctions that allow advertisers to bid on a per-impression or a per-click basis for the same advertising space. This paper studies the properties of equilibrium and considers how to increase efficiency in this new auction format. Rational expectations require the publisher to consider past bid types to prevent revenue losses to strategic advertiser behavior. The equilibrium results contradict publisher statements and suggest that, conditional on setting rational expectations, publishers should consider offering multiple bid types to advertisers. For a special case of the model, we provide a payment scheme that achieves the socially optimal allocation of advertisers to slots and maximizes publisher revenues within the class of socially optimal payment schemes. When this special case does not hold, no payment scheme will always achieve the social optimum.