AI 中文总结
该研究探讨广义首价拍卖的纯策略均衡存在性，发现广告排序依据改变时经典结论会反转，且其纯策略均衡下的期望收益可能高于或低于广义次价拍卖。
AI 中文摘要
我们重新审视了赞助搜索广告中广义首价拍卖（Generalized First-Price Auction）纯策略纳什均衡（非）存在性的经典结论，证明了当广告基于随机质量分与出价金额的乘积排序，而非仅基于出价或出价与确定性质量分的乘积排序时，该结论可能反转。此外，广义首价拍卖纯策略均衡下的期望收益可能大幅超过广义次价拍卖（Generalized Second-Price Auction），尽管部分条件下二者关系也可能反转。
英文摘要
We revisit the classic result on the (non-)existence of pure-strategy Nash equilibria in the Generalized First-Price Auction for sponsored search advertising and show that the conclusion may be reversed when ads are ranked based on the product of stochastic quality scores and bid amounts, rather than solely on the bids or on the product of bids and deterministic quality scores. Moreover, the expected revenue in the pure strategy equilibrium of the Generalized First-Price Auction may substantially exceed that of the Generalized Second-Price Auction, although under some conditions the relation may also be reversed.
