Abstract
We develop a Bayes-Nash analysis of the Generalized Second Price (GSP) auction. First, we characterize the efficient Bayes-Nash equilibrium of the GSP when such an equilibrium exists. We obtain sufficient conditions on click-through rates that guarantee existence and show that an efficient equilibrium may fail to exist if click-through rates across slots are sufficiently close. Next, we derive the counter-intuitive result that the seller's revenue may decrease as click-through rates increase. Fortunately, we show that setting optimal reserve prices reverses this result. Further, we prove that the GSP possesses no mixed strategy equilibrium and that no inefficient equilibrium can be symmetric.
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