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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. 

Abstract The Jiamusi (JME) radar is the first high‐frequency coherent scatter radar independently developed in China. In this study, we investigate the statistical characteristics of the Jiamusi radar scattering occurrence rate from the F‐region ionosphere between 40°N and 65°N geomagnetic latitude (MLAT) from March 2018 to November 2019. Then, the diurnal and seasonal variations in scattering echoes and their dependence on geomagnetic conditions are statistically investigated. It is shown that the local time of the peak scattering occurrence rate varies depending on the seasons, that is, approximately 20–22.5 magnetic local time (MLT) in summer, 17.5–20.5 MLT in equinox, and 16–17.5 MLT in winter, which is closely associated with the time of sunset. The occurrence rate also increases with the enhancement of the Kp index. To further understand the mechanism of these features, we simulate the distribution of the gradient drift instability (GDI) indicatorby using the Thermosphere‐Ionosphere‐Electrodynamics General Circulation Model (TIEGCM). The analysis results indicate that the GDI may be one of the factors that contribute to these characteristic features. 

We consider a new problem of selling data to a machine learner who looks to purchase data to train his machine learning model. A key challenge in this setup is that neither the seller nor the machine learner knows the true quality of data. When designing a revenue-maximizing mechanism, a data seller faces the tradeoff between the cost and precision of data quality estimation. To address this challenge, we study a natural class of mechanisms that price data via costly signaling. Motivated by the assumption of i.i.d. data points as in classic machine learning models, we first consider selling homogeneous data and derive an optimal selling mechanism. We then turn to the sale of heterogeneous data, motivated by the sale of multiple data sets, and show that 1) on the negative side, it is NP-hard to approximate the optimal mechanism within a constant ratio e/(e+1) + o(1); while 2) on the positive side, there is a 1/k-approximate algorithm, where k is the number of the machine learner’s private types.