document: On revenue in the generalized second price auction The Generalized Second Price ( GSP ) auction is the primary auction used for selling sponsored search advertisements . In this paper we consider the revenue of this auction at equilibrium . We prove that if agent values are drawn from identical regular distributions , then the GSP auction paired with an appropriate reserve price generates a constant fraction ( 1\/6th ) of the optimal revenue . In the full-information game , we show that at any Nash equilibrium of the GSP auction obtains at least half of the revenue of the VCG mechanism excluding the payment of a single participant . This bound holds also with any reserve price , and is tight . Finally , we consider the tradeoff between maximizing revenue and social welfare . We introduce a natural convexity assumption on the click-through rates and show that it implies that the revenue-maximizing equilibrium of GSP in the full information model will necessarily be envy-free . In particular , it is always possible to maximize revenue and social welfare simultaneously when click-through rates are convex . Without this convexity assumption , however , we demonstrate that revenue may be maximized at a non-envy-free equilibrium that generates a socially inefficient allocation .
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