Bayes-Nash Equilibria of the Generalized Second Price Auction
对搜索引擎用于出售赞助广告位的广义第二价格拍卖进行贝叶斯-纳什分析，刻画了有效均衡的存在条件，发现点击率接近时有效均衡可能不存在，并得出卖家收入可能随中间位置点击率上升而下降的反直觉结论，但最优保留价可逆转此结果。
In this paper we develop a Bayes-Nash analysis of the Generalized Second Price (GSP) auction, the mechanism used by search engines to sell sponsored advertising positions. Interestingly, our results are in sharp contrast with the previous literature that adopts a complete information framework. First, we characterize the efficient Bayes-Nash equilibrium of the GSP when such an equilibrium exists. We then 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 of the second to last slots increase, provided the distribution of advertisers' values per click is concentrated on high values. 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.