Competing auctions with non-identical objects

Abstract

We study a competition model with two sellers that auction non-identical objects, unlike most of the literature on competing auctions. Each bidder has bidimensional private information, his values for the objects, and chooses the auction in which he participates (if any) after each seller has set a reserve price for her auction. We show that in some cases the duopoly reserve price is greater than the reserve price for a monopolist auctioning a single object; thus, an increase in the number of sellers may make some bidder’s types worse off. In our analysis we first characterize the unique symmetric equilibrium for the game of auction choice played by the bidders and investigate its features. Then for the game of reserve price setting played by the sellers, we show that in each symmetric equilibrium the reserve price level is determined by the interplay of two effects, a virtual value effect and a business stealing effect. The former tends to lift the equilibrium reserve price above the monopoly level, the latter may drive the equilibrium reserve price significantly below the monopoly level when the number n of bidders is small. For a large n we find that different reserve prices in the two auctions have little effect on bidders’ auction choices. As a consequence, when n is large the business stealing effect weakens with respect to the virtual value effect, and for the cases we consider the equilibrium reserve price is above the monopoly level.