Budget-Constrained Auctions with Unassured Priors

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.