  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.
