When Gray Markets Have Silver Linings: All-Unit Discounts, Gray Markets, and Channel Management
Bibliographic record
Abstract
Gray markets are unauthorized channels of distribution for a supplier's authentic products. We study a distribution channel that consists of a supplier who offers all-unit quantity discounts for batch orders to enjoy cost savings, and a reseller who may divert some goods to the gray markets. We show that the impact of gray markets depends on the reseller's inventory holding cost. When the reseller's inventory holding cost is high, diversion to the gray markets improves the channel performance by enabling the reseller to make batch orders. Because the reseller's order costs decrease through quantity discounts, diversion to the gray markets reduces the resale price and expands sales to the authorized channel. On the other hand, when the reseller's inventory holding cost is low, the reseller would make the batch orders even without the gray markets. In this case the diversion to the gray markets may improve the reseller's performance by shortening the order cycles and reducing the inventory holding costs. Interestingly, because diversion to the gray markets decreases the reseller's cycle inventory volume, the reseller has the reduced incentive to push its inventory, and, consequently, the resale price rises and sales volume decreases in the authorized channel. Moreover, there exists a range of reseller's inventory holding cost and supplier's cost of scale economy such that it is optimal for the supplier to induce reseller's gray market diversion through an all-unit discount. We show that these results are robust when the gray market overlaps with the authorized channel or when the gray market price is sensitive to reseller's diversion volume.
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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) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.002 | 0.003 |
| Scholarly communication | 0.004 | 0.007 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.003 | 0.003 |
| Insufficient payload (model declined to judge) | 0.011 | 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".