Coasian equilibria in sequential auctions

We study stationary equilibria in a sequential auction setting. A seller runs a sequence of standard first-price or second-price auctions to sell an indivisible object to potential buyers. The seller can commit to the rule of the auction and the reserve price of the current period but not to reserve prices of future periods. We prove the existence of stationary equilibria and establish a uniform Coase conjecture-as the period length goes to zero, the seller's profit from running sequential auctions converges to the profit of running an efficient auction uniformly across all points in time and all symmetric stationary equilibria.