In the basic auction model, the optimal reserve price may depend on the number of bidders

Article 105371. Abstract: A widespread claim in the auction literature about the most well known auction setting with i.i.d. private values is that the optimal reserve price for a second price auction is independent of the number nof bidders. This is indeed the case if the virtual valuation function is increasing, but this result fails to hold if the virtual valuation is non-monotone. In such case the optimal reserve price is weakly increasing in nand, as ntends to infinity, it tends to the highest regular valuation with zero virtual value.