Competition in price and availability when availability is unobservable

I present a strategic model of competition in price and availability in which demand is uncertain and consumers choose where to shop given firms' observable prices and their expectations of firms' unobservable inventories. In both a single-period Cournot model (inventories are chosen first) and a single-period Bertrand model (prices are chosen first), I show that firms use higher prices to "signal" higher availability. This creates a floor on equilibrium prices and industry profits regardless of the number of firms. The model is useful in understanding the relationship between price and availability in the video rental industry.