Competing Auctions with Non-Identical Objects

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 characterize the unique symmetric equilibrium for the game of auction choice played by the bidders and investigate its features. For the game of reserve price setting played by the sellers, in each symmetric equilibrium the reserve price level is determined by the interplay of two effects, a participation effect which tends to lift the equilibrium reserve price above the monopoly level, and a business stealing effect. The latter may drive the equilibrium reserve price significantly below the monopoly level when the number n of bidders is small, but 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, and for the cases we consider the equilibrium reserve price is above the monopoly level. This implies that some bidder types are worse off under duopoly than under monopoly