Structural Properties of Buyback Contracts for Price-Setting Newsvendors
Bibliographic record
Abstract
This paper studies a buyback contract in the Stackelberg framework of a manufacturer (leader) selling to a price-setting newsvendor retailer (follower). Using an analytical model that focuses on a multiplicative demand form, we generalize previous results and produce new structural insights. A novel transformation technique first enables us to establish the unimodality of the profit functions for both channel partners, under relatively mild assumptions. Further analysis identifies the necessary and sufficient condition under which the optimal contract for the manufacturer (wholesale and buyback prices) is distribution free, i.e., independent of the uncertainty in customer demand. A specific instance of the above condition is also necessary and sufficient for a no-buyback contract to be optimal from the manufacturer's perspective. We then prove that the optimal performance of the decentralized channel for distribution-free buyback contracts depends only on the curvature of the deterministic demand part. In addition, some of the optimal decisions and relevant profit ratios for buyback contracts in our setting are shown to be identical to those for their deterministic price-only counterparts.
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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 | 0.005 | 0.022 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.002 | 0.005 |
| Scholarly communication | 0.004 | 0.008 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.003 | 0.004 |
| Insufficient payload (model declined to judge) | 0.012 | 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".