We study dynamic price competition between sellers offering differentiated products with limited capacity and a common sales deadline. In every period, firms simultaneously set prices, and a randomly arriving buyer decides whether to purchase a product or leave the market. Given remaining capacities, firms trade off selling today against shifting demand to competitors to obtain future market power. We provide conditions for the existence and uniqueness of pure-strategy Markov perfect equilibria. In the continuous-time limit, prices solve a system of ordinary differential equations. We derive properties of equilibrium dynamics and show that prices increase the most when the product with the lowest remaining capacity sells. Because firms do not fully internalize the social option value of future sales, equilibrium prices can be inefficiently low such that both firms and consumers would benefit if firms could commit to higher prices. We term this new welfare effect the Bertrand scarcity trap.
We introduce a model of dynamic pricing in perishable goods markets with competition and provide conditions for equilibrium uniqueness. Pricing dynamics are rich because both own and competitor scarcity affect future profits. We identify new competitive forces that can lead to misallocation due to selling units too quickly: the Bertrand scarcity trap. We empirically estimate our model using daily prices and bookings for competing U.S. airlines. We compare competitive equilibrium outcomes to those where firms use pricing heuristics based on observed internal pricing rules at a large airline. We find that pricing heuristics increase revenues (4-5%) and consumer surplus (3%).