Optimal Marketing Strategies for the Acquisition and Retention of Service Subscribers
Bibliographic record
Abstract
In this paper, we propose a diffusion model for a subscription service. The evolution over time of the number of subscribers is governed by a differential equation combining two processes—namely, a customer acquisition process and a customer attrition process. Assuming profit-maximization behavior of the firm, we use dynamic programming to optimize the customer equity and determine optimal customer relationship marketing expenditures. We implement an augmented Kalman filter with continuous state and discrete observations to estimate the model’s parameters using market data of two well-known companies in the telecommunications sector. To the best of our knowledge, this is the first paper to model acquisition and retention efforts in the context of a diffusion model. By doing so, we extend the literature on product diffusion to services—that is, beyond its traditional area of durable (and occasionally nondurable) products. By the same token, we contribute to the literature on customer relationship marketing (CRM), where social interactions have been overlooked. Our analytical and numerical results provide a better understanding of the relationships among the optimal customer equity, the customer lifetime value, the prospect lifetime value, and the optimal acquisition and retention spending. Our model and estimation approach give the tools for assessing empirically the role of CRM spending, social interactions, and other factors in the service subscription dynamics. Our main empirical results are as follows: (i) CRM spending and external incentives have indeed a significant effect on acquisition and retention processes; (ii) the impact of CRM is market specific; (iii) compared with optimal levels, both firms underinvest in retention; and (iv) whereas we observe increasing spending in acquisition over time, the derived optimal policy recommends a decreasing level of spending over time. This paper was accepted by Eric Anderson, marketing.
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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 | 0.001 | 0.006 |
| Meta-epidemiology (narrow) | 0.000 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.006 | 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".