Dynamic Pricing in the Presence of Heterogeneous Social Influence

We study a firm’s dynamic pricing problem in a continuous-time setting where multiple market segments learn the product quality from post-purchase customer opinions and exert heterogeneous levels of social influence on other segments. The optimal solution is not always unique due to the conflicting objectives of revenue maximization and information revelation. When social influences strengthen, the revenue maximization solution shifts towards (or away from) the information revelation solution to achieve the optimal outcome for the high-quality (or low-quality) product. We also show that post-purchase opinions from each segment reveal the true product quality, and if customers can consistently access these opinions, they will fully understand the product quality. A numerical study demonstrates that segment-specific pricing strategies differ notably depending on whether the segment is influential. Compared to static and undifferentiated dynamic pricing policies, the segment-differentiated policy extracts less revenue from the influential segment and focuses more on controlling its information revelation role. Furthermore, failing to recognize distinctive segments and perform price differentiation by segment can cause nontrivial revenue loss. Finally, we measure and track the revenue impact of a single unit of opinion on a segment over time, finding it critical in determining the (non-)uniqueness of the optimal solution. Although the revenue impact on the influential segment is low due to its small size, it exerts a high impact on the entire market