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 for a click -- but only affect the auction's allocation and payment rule. This makes information design effectively a (constrained) mechanism design problem. We primarily focus on the two-bidder situation, which is already notoriously challenging as demonstrated in recent works, and adopt the algorithmic lens of developing approximate algorithms. Our first result is an FPTAS to compute an approximately optimal mechanism. The design of this algorithm leverages Bayesian bidder values which help to ``smooth'' the seller's revenue function and lead to better tractability. Our second result seeks to design ``simple'' and more practical signaling schemes. When bidders' CTR distribution is symmetric, we develop a simple prior-free signaling scheme, whose construction relies on a single parameter called 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：我们研究点击率拍卖中的信息设计问题，在该拍卖中，竞标者/广告商竞标赢得展示广告的机会，但仅对实际发生的点击付费。付费可能发生也可能不发生，其概率被称为点击率。这种拍卖形式广泛应用于在线广告行业。竞标者拥有私有价值，而卖方拥有关于每个竞标者点击率的私有信息。我们关注卖方通过部分揭示点击率信息以最大化收益的问题。点击率拍卖中的信息设计被证明与该领域几乎所有先前研究存在显著差异，因为任何关于点击率的已揭示信息都不会影响竞标者的出价行为——他们始终会对一次点击出价真实价值——而仅会影响拍卖的分配和支付规则。这使得信息设计本质上成为（约束条件下的）机制设计问题。我们主要聚焦于双竞标者情形——如近期研究所展示的，这本身已极具挑战性——并采用开发近似算法的算法视角。我们的第一个结果是提出一个用于计算近似最优机制的全多项式时间近似方案。该算法的设计利用了贝叶斯竞标者价值，这有助于"平滑"卖方的收益函数并提升可解性。我们的第二个结果旨在设计"简单"且更实用的信号方案。当竞标者的点击率分布对称时，我们开发了一个简单的无先验信号方案，其构造依赖于一个称为最优信号比的单一参数。只要竞标者价值密度函数的最大值与最小值差异不大，该构造方案即可证明获得良好的近似效果。