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