{'fraction_non_alphanumeric': 0.026781202627589692, 'fraction_numerical': 0.0, 'mean_word_length': 5.366559485530547, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
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 control methods to ensure that an advertiser’s payment is within her budget. Most budget control methods rely on the value distributions of advertisers. However, the platform hardly learns their true priors due to the complex environment advertisers stand in and privacy issues. 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 the bid-discount ﬁrst-price auction we introduce 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 surprising 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 thor-ough understanding of prior dependency in repeated auctions with budgets. The bid-discount ﬁrst-price