Competition over Price and Service Rate when Demand is Stochastic: A Strategic Analysis

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Abstract
We consider a two-stage game in which firms simultaneously select prices and capacities (or equivalently, outputs). Then, a random number of consumers attend the market, and each consumer selects a firm to visit. Consumers know all prices and quantities but not the realization of aggregate demand. The probability of being served at any firm depends on its capacity and the mixed strategy chosen by consumers. Consumers distribute themselves across firms so as to equalize the utility of each price-service pair. We show that there exists at most one equilibrium in which firms choose pure strategies, and characterize the "candidate" equilibrium. Consumers face a probability of being rationed, firms may have excess inventory, and the price remains above marginal cost. When there are many firms, the candidate is shown to be an equilibrium.
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