Dynamic Pricing Under Self-Exciting Arrival Processes

49 Pages Posted: 12 Jul 2024

See all articles by Quan Yuan

Quan Yuan

Zhejiang University

Longyuan Du

University of San Francisco - School of Management

Ming Hu

University of Toronto - Rotman School of Management

Date Written: July 09, 2024

Abstract

We study dynamic pricing under a stochastic, non-linear, self-exciting demand arrival process over a finite sales horizon. We adopt such a correlated demand process to capture the phenomenon that customers who have made a purchase can inform and excite future customers to arrive. Specifically, the stochastic arrival intensity is stimulated with an immediate boost after any purchase and gradually decays over time between two consecutive purchases. The arrival intensity is also affected by the market phase the seller operates in, a growth or maturity stage, which convexly or concavely shapes how many new customers informed customers can stimulate. We show that the optimal pricing policy depends on the current time and excitement level, which measures the currently accumulated influence that previously informed customers exert and is shown to be the only sufficient statistic for our problem. Over time, the seller tends to initially set a low price to attract early customers who can excite later arrivals and later increase the price to maximize profits. Perhaps surprisingly, for a given time, in the growth stage of the market, the optimal price rises with the excitement level, and conversely, in the maturity stage of the market, the optimal price drops with the excitement level. Moreover, we show that adopting the optimal time-varying (open-loop) pricing policy solved from the deterministic problem (without resolving the problem) leads to only a constant performance loss from the optimal dynamic (i.e., contingent) pricing policy, which would not hold for the classic revenue management problem with a capacity constraint. Finally, we extend our analysis to account for general information dissemination, discrete prices, and multiple products in an assortment.

Suggested Citation

Yuan, Quan and Du, Longyuan and Hu, Ming, Dynamic Pricing Under Self-Exciting Arrival Processes (July 09, 2024). Available at SSRN: https://ssrn.com/abstract=4889448 or http://dx.doi.org/10.2139/ssrn.4889448

Quan Yuan

Zhejiang University ( email )

38 Zheda Road
Hangzhou, Zhejiang 310058
China

Longyuan Du

University of San Francisco - School of Management ( email )

San Francisco, CA 94117
United States

Ming Hu (Contact Author)

University of Toronto - Rotman School of Management ( email )

105 St. George st
Toronto, ON M5S 3E6
Canada
416-946-5207 (Phone)

HOME PAGE: http://ming.hu

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