SHELF-SPACE ALLOCATION AND ADVERTISING DECISIONS IN THE MARKETING CHANNEL: A DIFFERENTIAL GAME APPROACH
Bibliographic record
Abstract
This paper deals with the issue of shelf-space allocation and advertising decisions in marketing channels. We consider a network composed of a unique retailer offering the products of two competing manufacturers. The retailer controls the amount of shelf-space to allocate to both brands, while the manufacturers make advertising decisions in order to build their brand image (i.e. the goodwill stock). The demand for each brand is affected by its own goodwill level and the shelf-space allocated to the brand at retailer's store. The problem is formulated as a Stackelberg differential game played over an infinite horizon, with the manufacturers as leaders and the retailer as the follower. Stationary feedback equilibria are computed. Our main results indicate that the shelf-space allocated to each brand, manufacturers' advertising strategies at the equilibrium and channel members' value functions are affected by the goodwill levels of both products.
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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 | 0.002 | 0.006 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.004 | 0.005 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.003 | 0.002 |
| Insufficient payload (model declined to judge) | 0.005 | 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 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".