We study autobidding ad auctions with user costs, where each bidder is value-maximizing subject to a return-over-investment (ROI) constraint, and the seller aims to maximize the social welfare taking into consideration the user's cost of viewing an ad. We show that in the worst case, the approximation ratio of social welfare by running the vanilla VCG auctions with user costs could as bad as 0. To improve the performance of VCG, We propose a new variant of VCG based on properly chosen cost multipliers, and prove that there exist auction-dependent and bidder-dependent cost multipliers that guarantee approximation ratios of 1/2 and 1/4 respectively in terms of the social welfare.

翻译：我们研究了包含用户成本的自动竞价广告拍卖场景，每个竞标者在投资回报率（ROI）约束下追求价值最大化，而卖方则旨在考虑用户观看广告成本的前提下最大化社会福利。我们证明，在最坏情况下，使用带有用户成本的原始VCG拍卖所获得的社会福利近似比可能低至0。为改善VCG拍卖的表现，我们提出了一种基于适当成本乘数的VCG变体，并证明存在依赖于拍卖和竞标者的成本乘数，分别能保证社会福利达到1/2和1/4的近似比。