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We present a dynamic pricing model for oligopolistic firms selling differentiated perishable goods to multiple finite segments of strategic consumers who are aware that pricing is dynamic and may time their purchases accordingly. This model encompasses strategic behavior by both firms and consumers in a unified stochastic dynamic game in which each firm's objective is to maximize its total expected revenues, and each consumer responds according to a shopping-intensity-allocation consumer choice model. We prove the existence of a unique subgame-perfect equilibrium, provide equilibrium optimality conditions, and prove monotonicity results for special cases. The model provides insights about equilibrium price dynamics under different levels of competition, asymmetry between firms, and multiple market segments with varying properties. We demonstrate that strategic behavior by consumers can have serious impacts on revenues if firms ignore that behavior in their dynamic pricing policies. Moreover, ideal equilibrium responses to consumer strategic behavior can recover only a portion of the lost revenues. A key conclusion is that firms may benefit more from limiting the information available to consumers than from allowing full information and responding to the resulting strategic behavior in an optimal fashion.
Levin et al. (Thu,) studied this question.