We propose and study a novel mechanism design setup where each bidder holds two kinds of private information: (1) type variable, which can be misreported; (2) information variable, which the bidder may want to conceal or partially reveal, but importantly, not to misreport. We refer to bidders with such behaviors as strategically reticent bidders. Among others, one direct motivation of our model is the ad auction in which many ad platforms today elicit from each bidder not only their private value per conversion but also their private information about Internet users (e.g., user activities on the advertiser's websites) in order to improve the platform's estimation of conversion rates. We show that in this new setup, it is still possible to design mechanisms that are both Incentive and Information Compatible (IIC). We develop two different black-box transformations, which convert any mechanism $\mathcal{M}$ for classic bidders to a mechanism $\bar{\mathcal{M}}$ for strategically reticent bidders, based on either outcome of expectation or expectation of outcome, respectively. We identify properties of the original mechanism $\mathcal{M}$ under which the transformation leads to IIC mechanisms $\bar{\mathcal{M}}$. Interestingly, as corollaries of these results, we show that running VCG with bidders' expected values maximizes welfare, whereas the mechanism using expected outcome of Myerson's auction maximizes revenue. Finally, we study how regulation on the auctioneer's usage of information can lead to more robust mechanisms.

翻译：我们提出并研究了一种新颖的机制设计框架，其中每位投标者持有两类私人信息：(1) 类型变量，可被虚报；(2) 信息变量，投标者可能希望隐瞒或部分披露，但关键是不能虚报。我们将具有此类行为的投标者称为“战略性缄默投标者”。该模型的一个直接动机来自广告拍卖：当前许多广告平台不仅需要投标者提供每次转化的私人估值，还需提供关于互联网用户（如广告主网站上的用户活动）的私人信息，以改进平台对转化率的估计。我们证明，在这一新框架下，依然可以设计同时满足激励相容与信息相容（IIC）的机制。我们开发了两种不同的黑箱转换方法，分别基于“期望结果”和“结果的期望”，将针对经典投标者的任意机制$\mathcal{M}$转换为面向战略性缄默投标者的机制$\bar{\mathcal{M}}$。我们确定了原始机制$\mathcal{M}$需满足的特性，使得转换后的机制$\bar{\mathcal{M}}$实现IIC。有趣的是，作为这些结果的推论，我们发现采用投标者期望值的VCG机制可最大化社会福利，而采用迈尔森拍卖期望结果的机制可最大化收益。最后，我们研究了拍卖方信息使用监管如何导向更稳健的机制。