Sequential Auctions with Randomly Arriving Buyers

We analyze a dynamic market in which buyers compete in a sequence of auctions for common value or differentiated goods. New buyers and objects may arrive at random times. Since objects are imperfect substitutes, buyers’ private values are not persistent. Instead, buyers receive new signals or draw new values in each period.

We consider the use of second-price auctions for selling these objects. In equilibrium, buyers do not bid their true expected values. Instead, they shade their bids down by their continuation value, which is the option value of participating in future auctions. We show that this option value depends not only on the number of buyers currently present on the market, but also on anticipated market dynamics. In particular, the option value also depends on the arrival rates on both sides of the market. We extend our results to the setting in which objects come from different distributions and market conditions evolve, with some persistence, as in a “buyer’s market” or a “seller’s market.”