Dynamic Pricing Under Self-Exciting Arrival Processes

Pricing with a Ripple Effect How should firms price when each sale sparks the next? In their paper, “Dynamic Pricing Under Self-Exciting Arrival Processes,” Quan Yuan, Longyuan Du, and Ming Hu study pricing decisions in markets where customer purchases actively stimulate future demand through word-of-mouth and social influence. Using a self-exciting (Hawkes) process to model the demand process, the authors show that optimal prices depend on both time and an “excitement level” summarizing accumulated customer influence. A key insight is that optimal prices may rise or fall with demand momentum, depending on whether the market is in a growth or saturation phase. The paper further demonstrates that simple, easy-to-implement deterministic (nonstationary) pricing heuristics can perform nearly as well as fully dynamic policies at large demand volumes. These results provide actionable guidance for firms operating in social media–driven markets, where this hour’s customers shape the next hour’s demand, and highlight the importance of explicitly accounting for the ripple effect of purchases in pricing design.