Equilibrium Reserve Prices in Sequential Ascending Auctions

Bernard Caillaud and Claudio Mezzetti

Abstract





 
We study a model in which the same set of bidders, with perfectly correlated valuations across units, compete for two units of a good in two sequential ascending-price auctions. The seller sets a reserve price before the beginning of each auction. Surprisingly, the equilibrium has a simple structure; strategic non-disclosure of information (i.e., pooling) only takes the form of non-participation in the early auction by bidders with valuations below a threshold, while bidders with valuations above the threshold participate and bid truthfully; that is, they stay in the auction until the price reaches their true valuations. The participation threshold is strictly higher than the reserve price in the first auction, so some buyers who would find it profitable to buy at the reserve price select not to participate in order to attempt to decrease the reserve price in the second auction. Participation in the first auction is lower than under full commitment, but the probability of at least one bidder participating in the second auction is higher.

Keywords: repeated auctions, ratchet effect, participation, reserve price.

JEL: D44, D82.