In today's online advertising markets, it is common for advertisers to set long-term budgets. Correspondingly, advertising platforms adopt budget control methods to ensure that advertisers' payments lie within their budgets. Most budget control methods rely on the value distributions of advertisers. However, due to the complex advertising landscape and potential privacy concerns, the platform hardly learns advertisers' true priors. Thus, it is crucial to understand how budget control auction mechanisms perform under unassured priors. This work answers this problem from multiple aspects. We consider the unassured prior game among the seller and all buyers induced by different mechanisms in the stochastic model. We restrict the parameterized mechanisms to satisfy the budget-extracting condition, which maximizes the seller's revenue by extracting buyers' budgets as effectively as possible. Our main result shows that the Bayesian revenue-optimal mechanism and the budget-extracting bid-discount first-price mechanism yield the same set of Nash equilibrium outcomes in the unassured prior game. This implies that simple mechanisms can be as robust as the optimal mechanism under unassured priors in the budget-constrained setting. In the symmetric case, we further show that all these five (budget-extracting) mechanisms share the same set of possible outcomes. We further dig into the structural properties of these mechanisms. We characterize sufficient and necessary conditions on the budget-extracting parameter tuple for bid-discount/pacing first-price auctions. Meanwhile, when buyers do not take strategic behaviors, we exploit the dominance relationships of these mechanisms by revealing their intrinsic structures.

翻译：在当今在线广告市场中，广告主设定长期预算的做法十分普遍。相应地，广告平台采用预算控制方法来确保广告主的支付不超过其预算。大多数预算控制方法依赖于广告主的价值分布。然而，由于复杂的广告环境和潜在的隐私问题，平台难以获知广告主的真实先验信息。因此，理解预算控制拍卖机制在未确知先验下的表现至关重要。本文从多个方面回答了这一问题。我们考虑了随机模型中不同机制引发的卖家和所有买家之间的未确知先验博弈。我们将参数化机制限制为满足预算提取条件，该条件通过尽可能有效地提取买家预算来最大化卖家收益。我们的主要结果表明，贝叶斯收益最优机制与预算提取竞价折扣一价机制在未确知先验博弈中产生相同的纳什均衡结果集合。这意味着在预算约束设置下，简单机制与最优机制在未确知先验下具有同等的稳健性。在对称情形下，我们进一步表明这五种（预算提取）机制共享相同的可能结果集合。我们还深入探讨了这些机制的结构性质。我们刻画了竞价折扣/调价一价拍卖的预算提取参数元组的充分必要条件。同时，当买家不采取策略行为时，我们通过揭示其内在结构来阐明这些机制的支配关系。