Notifications are important for the user experience in mobile apps and can influence their engagement. However, too many notifications can be disruptive for users. A typical mobile app usually has several types of notification, managed by distinct teams with objectives that are possibly conflicting with each other, or even with the overall platform objective. Therefore, there is a need for careful curation of notifications sent to users of these different types. In this work, we study a novel centralized approach for notification optimization, where we view the opportunities to send user notifications as items and types of notifications as buyers in an auction market. Furthermore, the auction setup is unique, and the platform has the ability to subsidize the bids from the notification types.
Using tools from fair division, we study the application of competitive equilibrium for addressing this problem. We show that an Eisenberg-Gale-style convex program allows us to find an allocation that is fair to all notification types in hindsight. Using the dual of the formulation, we present an online algorithm that allocates notifications via first-price auctions using a pacing-multiplier approach. Secondly, we introduce an approach based on second-price auctions and pacing, which has the benefit of working well with existing advertising systems built for second-price auctions.
Through an A/B test in production, we show that the second price-based auction system improves over a decentralized notification optimization system, leading to its launch in production for some Instagram notifications. Further, through simulations on Instagram notification data and a subsequent production A/B test, we compare the outcomes of first-price and second-price auctions and show that the former has more stable pacing multipliers.
先行拍卖（LA）是由Ronen提出的一种拍卖形式，用于在多个买家之间出售单个物品，它被认为比最优拍卖更简单，更公平。事实上，它通过对称的价格上升过程匿名选择一个临时赢家，然后才使用个性化的标价。一个LA拍卖提取至少1/2的最优收入，即使在相关的价值分布。这个界限是紧的，即使对于2个具有独立值的买家也是如此。我们引入了LA的一个自然扩展，称为lookahead with pooling（带池化的前瞻）。一个连续性拍卖作为LA进行，有一个区别：它允许卖方在价格上升阶段汇集一系列价值，并对它们一视同仁;因此，它保留了LA的简单性和公平性。我们的主要结果是，这种简单的池操作提高了独立买家的收入保证从1/2到4/7的最佳收入。我们还给出了一个互补的否定结果，表明对于任意相关先验，λ不能做得比1/2近似更好。
