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Auctioning with Strategically Reticent Bidders

Haifeng Xu
Jibang Wu
Conference submission (2021)


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 value type, which can be misreported; (2) private 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., their conversion history) in order to improve the platform’s estimation of all bidders’ 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 M for classic bidders to a mechanism M′ for strategically reticent bidders, based on either outcome of expectation or expectation of outcome, respectively. We identify properties of the original mechanismMunder which the transformation leads to IIC mechanismsM′ . 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.