In today's online advertising markets, it is common for an advertiser to set a long-period budget. Correspondingly, advertising platforms adopt budget management methods to control an advertiser's payment. Most budget control methods rely on the value distributions of advertisers. However, the platform hardly learns their true priors due to multiple reasons. Therefore, it is essential to understand how budget control auction mechanisms perform under unassured priors. This paper gives a two-fold answer. First, we introduce the bid-discount method into first-price auction. We show that the resulting auction mechanism exhibits desirable revenue maximization and computation properties. Second, we compare this mechanism with other four in the prior manipulation model, where an advertiser can arbitrarily report a value distribution to the platform. These four mechanisms include the optimal mechanism satisfying budget-constrained IC, first-price/second-price mechanisms with the widely-studied pacing method, and bid-discount second-price mechanism. We consider two different settings varying on whether the seller knows the reported value distributions before choosing the auction mechanism. When the reported priors are pre-known to the seller, we show that bid-discount first-price auction dominates the other four mechanisms concerning the platform's revenue. On the other hand, when the seller has no information on the reported priors before committing to a mechanism, we show a strategic-equivalence result between this mechanism and the optimal auction. When buyers are further symmetric, we establish a wide equivalence among variants of first-price and second-price auctions. Based on these findings, we provide a thorough understanding of prior dependency in repeated auctions with budgets. Bid-discount first-price auction itself may also be of further independent research interest.
翻译:在今天的在线广告市场中,广告商通常会设置长期的拍卖预算。 因此,广告平台会采用预算管理方法来控制广告商的付款。 大部分预算控制方法都依赖于广告商的价值分配。 但是,由于多种原因,平台几乎无法了解其真实的前科。 因此, 理解预算控制拍卖机制如何在未加肯定的预证的拍卖前期运作至关重要。 本文给出了双重答案。 首先, 我们将出价折扣方法引入了第一次价格拍卖。 我们显示, 由此形成的拍卖机制显示, 适当的收益最大化和计算属性。 其次, 我们将这一机制与其他四个前操纵模型中的高级等数据进行比较, 即广告商可以任意向平台报告价值分配情况。 这四个机制包括满足预算限制的IC的最佳机制, 第一价格/第二价格机制, 以及广泛审计的双价机制。 我们首先考虑两种不同的最佳环境, 卖方在选择拍卖机制之前是否知道所报的价值分配方式。 当报告之前, 我们先是知道的关于前期货价机制, 之后, 我们又会显示其他的股价机制。