We consider dynamic pricing competition between two firms offering vertically differentiated products to strategic customers who are intertemporal utility maximizers. We show that price skimming arises as the unique pure-strategy Markov perfect equilibrium in the game under a simple condition. Our results highlight the asymmetric effect of strategic customer behavior on quality-differentiated firms. Even though the profit of either firm decreases as customers become more strategic, the low-quality firm suffers substantially more than the high-quality firm. Furthermore, we show that unilateral commitment to static pricing by either firm generally improves profits of both firms. Interestingly, both firms enjoy higher profit lifts when the high-quality firm commits rather than when the low-quality firm commits.
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