Strategic bid-shading and sequential auctioning with learning from past prices

This paper analyzes sequential auctioning of single units of an indivisible good to a fluctuating population composed of overlapping generations of unit-demand bidders. Two phenomena emergent in such a market are investigated: forward-looking bidding strategies, and closed-loop selling strategies that involve learning from past prices. The buyers shade their bids down, i.e., bid less than they would in a single isolated auction, whenever they expect the seller to sell another unit of the good in the near future. Unlike in exogenous sequences of auctions, the optimal bidding strategy thus depends on the seller's selling strategy. The converse dependence also occurs: the seller can learn about current demand from past realized prices, and sell only in periods with high-enough demand. Such learning depends on the extent of bid-shading because the seller needs to invert the bidding strategy to learn. In equilibrium, buyer bid-shading persists even when the seller does not sell in every period, but it is self-regulating in that it eventually vanishes when the existence of the market is threatened by low seller profits. In this sense, auction markets have a ‘self-preservation instinct’. General properties of learning about current demand from past auction prices are also investigated and characterized.