Classic mechanism design often assumes that a bidder's action is restricted to report a type or a signal, possibly untruthfully. In today's digital economy, bidders are holding increasing amount of private information about the auctioned items. And due to legal or ethical concerns, they would demand to reveal partial but truthful information, as opposed to report untrue signal or misinformation. To accommodate such bidder behaviors in auction design, we propose and study a novel mechanism design setup where each bidder holds two kinds of information: (1) private \emph{value type}, which can be misreported; (2) private \emph{information variable}, which the bidder may want to conceal or partially reveal, but importantly, \emph{not} to misreport. We show that in this new setup, it is still possible to design mechanisms that are both \emph{Incentive and Information Compatible} (IIC). We develop two different black-box transformations, which convert any mechanism $\mathcal{M}$ for classic bidders to a mechanism $\mathcal{M}'$ 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 $\mathcal{M}'$. Interestingly, as corollaries of these results, we show that running VCG with expected bidder 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 may lead to more robust mechanisms.

中文翻译：

---

与策略性沉默的投标人一起拍卖

经典机制设计通常假设投标人的行为仅限于报告类型或信号，这可能是不真实的。在当今的数字经济中，投标人持有越来越多的关于拍卖物品的私人信息。出于法律或道德方面的考虑，他们会要求披露部分但真实的信息，而不是报告不真实的信号或错误信息。为了在拍卖设计中适应这种投标人的行为，我们提出并研究了一种新颖的机制设计设置，其中每个投标人都持有两种信息：（1）私人 \emph{价值类型}，这可能会被误报；(2) 私人\emph{信息变量}，投标人可能想要隐藏或部分透露，但重要的是，\emph{不要}误报。我们表明，在这个新设置中，仍然可以设计同时具有\emph{激励和信息兼容}（IIC）的机制。我们开发了两种不同的黑盒转换，根据预期结果或结果预期，将经典投标人的任何机制 $\mathcal{M}$ 转换为战略沉默投标人的机制 $\mathcal{M}'$，分别。我们确定原始机制 $\mathcal{M}$ 的属性，在该属性下，转换导致 IIC 机制 $\mathcal{M}'$。有趣的是，作为这些结果的推论，我们表明，以预期投标人价值运行 VCG 可使福利最大化，而使用 Myerson 拍卖预期结果的机制可使收入最大化。最后，我们研究了对拍卖师信息使用的监管如何导致更强大的机制。