In recent years, the growing adoption of autobidding has motivated the study of auction design with value-maximizing auto-bidders. It is known that under mild assumptions, uniform bid-scaling is an optimal bidding strategy in truthful auctions, e.g., Vickrey-Clarke-Groves auction (VCG), and the price of anarchy for VCG is $2$. However, for other auction formats like First-Price Auction (FPA) and Generalized Second-Price auction (GSP), uniform bid-scaling may not be an optimal bidding strategy, and bidders have incentives to deviate to adopt strategies with non-uniform bid-scaling. Moreover, FPA can achieve optimal welfare if restricted to uniform bid-scaling, while its price of anarchy becomes $2$ when non-uniform bid-scaling strategies are allowed. All these price of anarchy results have been focused on welfare approximation in the worst-case scenarios. To complement theoretical understandings, we empirically study how different auction formats (FPA, GSP, VCG) with different levels of non-uniform bid-scaling perform in an autobidding world with a synthetic dataset for auctions. Our empirical findings include: * For both uniform bid-scaling and non-uniform bid-scaling, FPA is better than GSP and GSP is better than VCG in terms of both welfare and profit; * A higher level of non-uniform bid-scaling leads to lower welfare performance in both FPA and GSP, while different levels of non-uniform bid-scaling have no effect in VCG. Our methodology of synthetic data generation may be of independent interest.

翻译：近年来，自动出价的广泛采用推动了对价值最大化自动竞价者拍卖设计的研究。已知在温和假设下，均匀出价缩放是真实拍卖（如维克里-克拉克-格罗夫斯拍卖（VCG））中的最优竞价策略，且VCG的“无政府价格”为2。然而，对于其他拍卖格式如首价拍卖（FPA）和广义第二价格拍卖（GSP），均匀出价缩放可能并非最优竞价策略，竞标者具有偏离策略以采用非均匀出价缩放的动机。此外，若限制为均匀出价缩放，FPA可实现最优福利；但允许非均匀出价缩放策略时，其“无政府价格”变为2。所有这些“无政府价格”结果均聚焦于最坏情况下的福利近似。为补充理论理解，我们基于合成拍卖数据集，实证研究了不同拍卖格式（FPA、GSP、VCG）在不同非均匀出价缩放水平下的表现。实证发现包括：* 在均匀与非均匀出价缩放下，FPA在福利和利润方面均优于GSP，而GSP优于VCG；* 在FPA和GSP中，更高的非均匀出价缩放水平导致更低的福利表现，而不同非均匀出价缩放水平对VCG无影响。我们的合成数据生成方法可能具有独立研究价值。