Searching on a Deadline

We analyze an equilibrium search model where the buyer seeks to purchase a good before a deadline. The buyer's reservation price rises continuously as the deadline approaches. A seller cannot observe a potential buyer's remaining time until deadline, and hence posts a price that weighs the probability of sale versus the profit once sold. The model has a unique equilibrium, which can take exactly one of two forms. In a late equilibrium, buyers initially forgo any purchases, only accepting some offers as the deadline draws near. In an early equilibrium, buyers are willing to accept some offers even as they enter the market. Equilibrium price dynamics are determined by the concentration of buyers near their deadline, as well as their urgency of completing the transaction before their deadline.