Bibliographic record
Abstract
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 [Formula: see text] 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 .
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.004 | 0.020 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.004 | 0.005 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.002 | 0.002 |
| Insufficient payload (model declined to judge) | 0.009 | 0.001 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".