We study information design in click-through auctions, in which the bidders/advertisers bid for winning an opportunity to show their ads but only pay for realized clicks. The payment may or may not happen, and its probability is called the click-through rate (CTR). This auction format is widely used in the industry of online advertising. Bidders have private values, whereas the seller has private information about each bidder's CTRs. We are interested in the seller's problem of partially revealing CTR information to maximize revenue. Information design in click-through auctions turns out to be intriguingly different from almost all previous studies in this space since any revealed information about CTRs will never affect bidders' bidding behaviors -- they will always bid their true value per click -- but only affect the auction's allocation and payment rule. In some sense, this makes information design effectively a constrained mechanism design problem. Our first result is an FPTAS to compute an approximately optimal mechanism under a constant number of bidders. The design of this algorithm leverages Bayesian bidder values which help to ``smooth'' the seller's revenue function and lead to better tractability. The design of this FPTAS is complex and primarily algorithmic. Our second main result pursues the design of ``simple'' mechanisms that are approximately optimal yet more practical. We primarily focus on the two-bidder situation, which is already notoriously challenging as demonstrated in recent works. When bidders' CTR distribution is symmetric, we develop a simple prior-free signaling scheme, whose construction relies on a parameter termed optimal signal ratio. The constructed scheme provably obtains a good approximation as long as the maximum and minimum of bidders' value density functions do not differ much.

翻译：我们研究点击付费拍卖中的信息设计问题。在该拍卖中，投标方/广告商竞拍获得展示广告的机会，但仅按实际点击量付费。支付行为可能发生也可能不发生，其概率称为点击率（CTR）。这种拍卖形式在在线广告行业中得到广泛应用。投标方拥有私有估值，而卖方掌握每个投标方点击率的私有信息。我们关注卖方通过部分披露点击率信息来最大化收益的问题。点击付费拍卖中的信息设计与该领域几乎所有先前研究存在显著差异：任何披露的点击率信息都不会影响投标方的出价策略——他们始终按每次点击的真实价值出价——但会影响拍卖的分配与支付规则。从某种意义上说，这使得信息设计实质上成为一个受约束的机制设计问题。我们的第一个成果是提出一个全多项式时间近似方案（FPTAS），用于在常数个投标方情形下计算近似最优机制。该算法的设计通过引入贝叶斯投标方估值来“平滑”卖方收益函数，从而提升可解性。该FPTAS设计复杂且主要基于算法思想。第二个主要成果聚焦于设计既近似最优又更具实用性的“简单”机制。我们重点研究双投标方情形——正如近期研究所揭示的，该情形本身已极具挑战性。当投标方的点击率分布对称时，我们提出一种无先验信号的方案，其构造依赖于称为最优信号比的关键参数。只要投标方估值密度函数的最大值与最小值差异不大，所构造方案就能保证良好的近似性能。