Revenue Management with Forward-Looking Buyers

We consider a seller who wishes to sell multiple goods by a deadline, such as the end of a season. Potential buyers enter over time, are long-lived and form rational expectations, so can strategically time their purchases. At any point in time, profit is maximized by awarding the good to the buyer with the highest valuation exceeding a cutoff. These cutoffs are deterministic, depending only on the number of units and time remaining. Since the seller does not need to elicit all entrants’ values, she can implement the optimal mechanism in the continuous time limit by posting anonymous prices. These prices depend on the number of units and time remaining and, unlike the optimal cutoffs, the timing of previous sales. When incoming demand is decreasing over time, the optimal cutoffs satisfy a oneperiod-look-ahead property and prices are defined by an intuitive differential equation.