Revenue Management Under a Price Alert Mechanism

Many online platforms adopt a price alert mechanism to facilitate customers tracking price changes. This mechanism allows customers to register their valuation with the system if they find the price higher than their valuation. Once the price drops below the customers’ registered price, a message is sent to notify customers. This paper formulates the interaction between the seller and customers as a Markov decision process. We assume customers are patient and are willing to wait for K additional periods for the price to drop if the current price is high. We first analyze the model in which $K=1$ and find that the seller’s optimal policy has three properties: (i) the threshold property by which the seller uses a threshold to decide whether to accept or reject a registered price, (ii) the price-at-register property by which the seller sets the price at the customer’s registered level if the registered price exceeds the threshold, and (iii) the cyclic decreasing property by which the price trajectory under the optimal policy has a stochastic cyclic decreasing structure. Modified versions of these properties still hold for the general model in which K is large or when the waiting time is heterogeneous among customers. On the policy computation side, we propose a heuristic pricing policy based on the price-at-register property. Numerical results show that the policy achieves near-optimal performance on all cases tested. We also observe that the impact of the value of K on the optimal revenue is almost negligible in many cases, and this ensures that the policies derived under our model are robust to the misspecification of K. This policy can also be adapted to the model in which customer patience is different and achieves near-optimal performance. Lastly, we show the impact of the price alert mechanism on seller’s revenue, customer surplus, and social welfare.

This paper was accepted by Omar Besbes, revenue management and market analytics.

Funding: B. Jiang’s research is partially supported by the National Natural Science Foundation of China (NSFC) [Grants 72394364, 72171141, 72394363, and 72442013]. Z. Wang’s research is partially supported by the National Natural Science Foundation of China (NSFC) [Grants 72394361 and 72425013], the Guangdong Provincial Key Laboratory of Mathematical Foundations for Artificial Intelligence [2023B1212010001], and the 1+1+1 CUHK-CUHK(SZ)-GDSTC Joint Collaboration Fund [2025A0505000079].

Supplemental Material: The online appendix and data files are available at https://doi.org/10.1287/mnsc.2024.05665.