论文标题
贝叶斯广告拍卖中的公共信号
Public Signaling in Bayesian Ad Auctions
论文作者
论文摘要
我们研究贝叶斯AD扣的信号传导,其中投标者的估值取决于随机的,未知的自然状态。拍卖机制完全了解自然的实际状态,并且可以向竞标者发送信号,以披露有关国家的信息并增加收入。例如,一个状态可以集体编码仅是该机制已知的用户的某些功能,因为后者可以访问投标人无法获得的数据源。我们研究计算该机制应如何向竞标者发送信号以最大化收入的问题。据我们所知,虽然在更轻松的第二价格拍卖的设置中已经解决了这个问题,但我们的工作是第一个探索多个插槽的广告拍卖的工作。在本文中,我们关注公共信号传导和VCG机制,在这些机制下,投标人如实地报告了他们的估值。我们从一个负面结果开始,表明通常,即使竞标者的估值是该机制已知的,除非p = np,否则问题也不会接收PTA。本文的其余部分专门用于可以规避这种负面结果的设置。首先,我们证明,凭借已知的估值,当固定状态D或插槽数的数量固定时,确实可以在多项式时间内解决问题。此外,在同一环境中,我们为投标人单身的情况提供了一个FPTA,但是D和M可以是任意的。然后,我们切换到随机估值设置,其中根据某些概率分布将其随机绘制。在这种情况下,我们表明该问题承认了一个FPTA,PTA和QPTA,分别固定D时,M固定了D,并且竞标者的估值远离零。
We study signaling in Bayesian ad auctions, in which bidders' valuations depend on a random, unknown state of nature. The auction mechanism has complete knowledge of the actual state of nature, and it can send signals to bidders so as to disclose information about the state and increase revenue. For instance, a state may collectively encode some features of the user that are known to the mechanism only, since the latter has access to data sources unaccessible to the bidders. We study the problem of computing how the mechanism should send signals to bidders in order to maximize revenue. While this problem has already been addressed in the easier setting of second-price auctions, to the best of our knowledge, our work is the first to explore ad auctions with more than one slot. In this paper, we focus on public signaling and VCG mechanisms, under which bidders truthfully report their valuations. We start with a negative result, showing that, in general, the problem does not admit a PTAS unless P = NP, even when bidders' valuations are known to the mechanism. The rest of the paper is devoted to settings in which such negative result can be circumvented. First, we prove that, with known valuations, the problem can indeed be solved in polynomial time when either the number of states d or the number of slots m is fixed. Moreover, in the same setting, we provide an FPTAS for the case in which bidders are single minded, but d and m can be arbitrary. Then, we switch to the random valuations setting, in which these are randomly drawn according to some probability distribution. In this case, we show that the problem admits an FPTAS, a PTAS, and a QPTAS, when, respectively, d is fixed, m is fixed, and bidders' valuations are bounded away from zero.