Optimal Dynamic Advertising Policies in Digital and Traditional Channels: A Control-Theoretic Approach
Why this work is in the frame
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Bibliographic record
Abstract
This study applies optimal control theory to investigate a monopolistic firm’s optimal allocation of advertising efforts across digital and traditional channels. By considering the competitive relationship between advertising efforts in different channels in satisfying consumers’ informational needs, this study explicitly models their substitution effect. Furthermore, we propose an alternative approach to incorporate different decay rates of incremental goodwill in the two channels, allowing the system dynamics to be directly represented by the firm’s total goodwill without separating it into multiple channel-specific components. Technically, this approach leads to the system dynamics being governed by an integro-differential equation rather than an ordinary differential equation. Our analysis reveals that the marginal value of goodwill in the digital channel is greater than that in the traditional channel due to a lower decay rate. However, this comparative advantage of the digital channel progressively diminishes over time. As a result, the firm should always invest in digital advertising, while employing traditional advertising only when the comparative advantage of the digital channel becomes weak in later stages. When additionally considering the synergistic effect between the two channels, the optimal adoption timing of traditional advertising occurs earlier as the intensity of synergistic effect increases.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.002 | 0.004 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
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 it