Trilateral game and vertical collaboration models in a two-stage green supply chain with substitutable green products
Bibliographic record
Abstract
This paper explores the trilateral game and vertical collaboration model based on Stackelberg’s (manufacturer-leadership game) and Bertrand’s game-theoretical methodology for a two-stage green supply chain where the duopolistic manufacturers and the retailer are ecologically conscious. Both manufacturers produce and sell two substitutable green products through a common retailer. The selling prices and green levels (GLs) determine the demand for both green products. A game theoretical approach is implemented in the trilateral game model, and the result shows that the manufacturer with a bigger sales volume achieves superior performance in terms of earnings. In the vertical collaboration model, a manufacturer and retailer collaborate to optimize pricing issues, GLs, and profits. Two-player games among three participants are performed for this collaboration. The results of the vertical collaboration model show that the overall profit in vertical collaboration is greater than the sum of the individual profits corresponding to two participants in the trilateral game model. Whereas, the manufacturer outside the collaboration experiences a decline in profits. Further, a selection criterion of manufacturers is also developed to maximize the overall profit of the retailer. Finally, a numerical example and a sensitivity analysis are performed to demonstrate the model’s implementation and stability.
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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 | 0.004 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.003 | 0.003 |
| Open science | 0.003 | 0.002 |
| Research integrity | 0.003 | 0.002 |
| Insufficient payload (model declined to judge) | 0.007 | 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".