Intertemporal Price Discrimination via Randomized Promotions

93 Pages Posted: 22 Aug 2018 Last revised: 17 Nov 2022

See all articles by Hongqiao Chen

Hongqiao Chen

Nanjing University - School of Management and Engineering

Ming Hu

University of Toronto - Rotman School of Management

Jiahua Wu

Imperial College Business School

Date Written: November 21, 2019


Problem definition: The undesirable but inevitable consequence of running promotions is that consumers can be trained to time their purchases strategically. In this paper, we study randomized promotions, where the firm randomly offers discounts over time, as an alternative strategy of intertemporal price discrimination.

Methodology/results: We consider a base model where a monopolist sells a single product to a market with a constant stream of two market segments. The segments are heterogeneous in both their product valuations and patience levels. The firm pre-commits to a price distribution, and in each period, a price is randomly drawn from the chosen distribution. We characterize the optimal price distribution as a randomized promotion policy and show that it serves as an intertemporal price discrimination mechanism such that high-valuation customers would make a purchase immediately at a regular price upon arrival and low-valuation customers would wait for a random promotion. Compared against the optimal cyclic pricing policy, which is optimal within the strategy space of all deterministic pricing policies, the optimal randomized pricing policy beats the optimal cyclic pricing policy if low-valuation customers are sufficiently patient and the absolute discrepancy between high and low customer valuations is large enough. We extend the model in three directions. First, we consider the case where a portion of customers are myopic, who would never wait. We show that the existence of myopic customers is detrimental to the firm's profitability, and the expected profit from an optimal randomized pricing policy decreases as the proportion of myopic customers in the population increases. Second, we consider Markovian pricing policies where prices are allowed to be intertemporally correlated in a Markovian fashion. This additional maneuver allows the firm to reap an even higher profit when low-valuation customers are sufficiently patient, by avoiding consecutive promotions but on average running the promotion more frequently with a smaller discount size. Lastly, we consider a model with multiple customer segments and show that a two-point price distribution remains optimal and our conclusion from the two-segment base model still holds under certain conditions that are adopted in the literature.

Managerial implications: Our results imply that the firm may want to deliberately randomize promotions in the presence of forward-looking customers.

Keywords: randomized pricing, intertemporal discrimination, promotion, strategic consumers

Suggested Citation

Chen, Hongqiao and Hu, Ming and Wu, Jiahua, Intertemporal Price Discrimination via Randomized Promotions (November 21, 2019). Available at SSRN: or

Hongqiao Chen

Nanjing University - School of Management and Engineering ( email )

Nanjing, 210093

Ming Hu (Contact Author)

University of Toronto - Rotman School of Management ( email )

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


Jiahua Wu

Imperial College Business School ( email )

Tanaka Building
South Kensington Campus
London, SW7 2AZ
United Kingdom
02075949851 (Phone)


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