Dynamic Pricing Competition with Strategic Customers Under Vertical Product Differentiation

We consider dynamic pricing competition between two firms offering vertically differentiated products to strategic customers who are inter-temporal utility maximizers. Our model can be viewed as a competitive version of the classical model of Besanko and Winston (1990). We show that there exists a Markov perfect equilibrium (MPE) in mixed strategy in the game. Furthermore, we give a simple condition for the existence of a unique pure strategy MPE, which admits explicit recursive expressions. We obtain results when customers are myopic as a special case. The explicit characterization of equilibrium behavior allows us to conduct an extensive numerical study to demonstrate our results and gain insights into the problem. Extending known results in the monopolistic setting, we show that dynamic pricing is often undesirable for both firms when customers are strategic, even though it improves profits when customers are myopic. Our results emphasize the role of product quality and the value of price commitment. While both firms tend to suffer profit loss from strategic customer behavior, the low-quality firm often experiences profit loss that is orders of magnitude higher than that of the high-quality firm. The detrimental effects of dynamic pricing are almost fully realized, even when each firm only reduces price once. Furthermore, we study a version of the model where one firm unilaterally commits to static pricing and show that such commitment can be very valuable for the committing firm. Interestingly, when the low-quality firm commits to static pricing, the equilibrium profits are often higher for both firms.