Sequential auctions with imperfect quantity commitment

This paper studies sequential second price auctions with imperfect quantity commitment in environments involving single-unit demands, independent private values, and non-decreasing marginal costs. The paper characterizes the symmetric equilibrium strategy and demonstrates that the equilibrium price sequence is conditionally non-increasing, showing a downwards drift in cases in which the marginal cost exceeds the reserve price with positive probability. The paper also argues that unlike a strong seller who sets reserve prices strictly above marginal costs, a weak seller will typically prefer to commit to such inefficiently low reserve prices.