Competition in Price and Availability when Availability is Unobservable

Abstract

This paper presents a strategic model of competition in both price and availability when firms can publicly commit to prices but not inventories (or capacities). Demand is uncertain and firms stock out in equilibrium. Consumers choose where to shop on the basis of price and expected service rate (the probability of being served). In a one period model, I show that although firms cannot affect consumers' expectations of their service rates by increasing inventory, they can signal higher service rates with higher prices (regardless of whether price or inventory is chosen first). This extra incentive to raise price generates a floor on equilibrium prices and industry profits that exists regardless of the number of firms. When price is set before output, high prices create incentives for firm to hold more inventory. So rational consumers anticipate high priced firms will have higher service rates. Applications of this model to video rental competition and other retail competition are discussed. When output is set before price, high prices act as a signal of high availability. This equilibrium is the unique equilibrium satisfying the never-a-weak-best-response property. Rational consumers anticipate high priced firms will have higher service rates and that firms that deviate to low prices must have changed their availability as well. In a repeated game firms that maintain reputations for higher service rates may earn even higher profits.