Reserve price efficiency and competitive pressure in auctions

In this paper I analyze the reserve price efficacy of an auction, that is the relative value of the expected revenue increase induced by the optimal reserve price. I define the competitive pressure in an auction and the notion of one auction dominance over another auction in terms of competition level. After that I prove that the reserve price efficacy decays with respect to the increase of competition level. Finally I provide some examples of auction attributes, which monotonically affect the competition level.