Sequential Auctions with Randomly Arriving Buyers

We analyze a dynamic market in which buyers compete in a sequence of auctions. New buyers and objects may arrive at random times. Buyers' private values, however, are not persistent. Instead, buyers draw new values in every period; equivalently, objects are heterogeneous but are drawn from the same distribution. We consider the use of the second-price auction for selling these objects. In equilibrium, buyers do not bid their true value. 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. We also generalize our results to the setting in which values correspond to a "buyer's market" or a "seller's market" and market conditions evolve, with persistence, from one to the other.