Dynamic Pricing of an Expiring Item under Strategic Buyers with Stochastic Arrival

Abstract

We study the optimal dynamic pricing of an expiring ticket or voucher, sold by a time-sensitive seller to strategic buyers who arrive stochastically with private values. The expiring nature creates a conflict: the seller's urgency to sell before expiration drives price reductions, which in turn incentivize buyers to wait. We seek the seller's optimal pricing policy that resolves this tension. The main analytical challenge is that buyer type is two-dimensional (valuation and arrival time), which makes equilibrium intractable under general strategies. To address this, we introduce the Value-Based Threshold (VBT) strategy, a tractable framework that decouples these two dimensions. Using this framework, we prove equilibrium existence via an ordinary differential equation and provide a constructive procedure for its characterization. We then derive near-optimal pricing policies for two stylized regimes: a constant price in thin markets and a linear discount in thick markets. Numerical frontier analysis confirms these benchmarks and shows how optimal policy adapts as the seller's time sensitivity changes. Our findings clarify the conflict between quick sales and strategic waiting. Sellers facing thick markets or high time sensitivity benefit from linear discounts, while in thin markets a constant price neutralizes buyers' incentive to wait. We also show this simple policy remains robust across broad conditions. For patient sellers, a quasi-auction schedule that maintains a high price until a sharp final drop is most effective in aggregating demand.