Competing first-price and second-price auctions

Abstract

This paper theoretically investigates which auctions are selected by competing sellers when they can choose between first-price auctions and second-price auctions, and when homogeneously risk averse bidders endogenously enter one of the auctions. In order to study this, we first consider bidders’ entry decisions between exogenously given auctions. We find that there exists a symmetric entry equilibrium that is unique and is characterized by a mixed strategy, which depends on whether bidders exhibit constant, decreasing or increasing absolute risk aversion. In a next step, we endogenize the sellers’ choice of auctions. We show that competing sellers have a dominant strategy to select first-price auctions if bidders exhibit nondecreasing absolute risk aversion. If bidders exhibit decreasing absolute risk aversion, other equilibria may exist in which sellers select second-price auctions as well. For instance, we demonstrate that sellers may select second-price auctions if the distribution of private values is sufficiently skewed.