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The Empirical Revenue Maximization (ERM) is one of the most important pricelearning algorithms in auction design: as the literature shows it can learnapproximately optimal reserve prices for revenue-maximizing auctioneers in bothrepeated auctions and uniform-price auctions. However, in these applicationsthe agents who provide inputs to ERM have incentives to manipulate the inputsto lower the outputted price. We generalize the definition of anincentive-awareness measure proposed by Lavi et al (2019), to quantify thereduction of ERM's outputted price due to a change of $m\ge 1$ out of $N$ inputsamples, and provide specific convergence rates of this measure to zero as $N$goes to infinity for different types of input distributions. By adopting thismeasure, we construct an efficient, approximately incentive-compatible, andrevenue-optimal learning algorithm using ERM in repeated auctions againstnon-myopic bidders, and show approximate group incentive-compatibility inuniform-price auctions.

A Game-Theoretic Analysis of the Empirical Revenue Maximization Algorithm with Endogenous Sampling