On Determination of Optimal Reserve Price in Auctions with Common Knowledge about Ranking of Valuations

Abstract

This paper investigates a case study in designing auctions with optimal reserve prices when an analytical solution for the equilibrium bid functions does not exist. The Runge-Kutta integration method nested in a backward-shooting algorithm is used to solve the equilibrium bid functions for a Þrst-price auction with bidders whose value ranking is common knowledge. The optimal reserve price is determined after a numerical search for the seller's maximum average revenue using simulated auction markets at equilibrium. We observe that setting the optimal reserve price can continue to raise, on average, more revenue for the seller in the Þrst-price auction than in the second-price auction.