Optimal Design of a Pharmaceutical Price–Volume Agreement Under Asymmetric Information About Expected Market Size
Bibliographic record
Abstract
Price–volume agreements are commonly negotiated between drug manufacturers and third‐party payers for drugs. In one form a drug manufacturer pays a rebate to the payer on a portion of sales in excess of a specified threshold. We examine the optimal design of such an agreement under complete and asymmetric information about demand. We consider two types of uncertainty: information asymmetry, defined as the payer's uncertainty about mean demand; and market uncertainty, defined as both parties' uncertainty about true demand. We investigate the optimal contract design in the presence of asymmetric information. We find that an incentive compatible contract always exists; that the optimal price is decreasing in expected market size, while the rebate may be increasing or decreasing in expected market size; that the optimal contract for a manufacturer with the highest possible demand would include no rebate; and, in a special case, if the average reservation profit is non‐decreasing in expected market size, then the optimal contract includes no rebates for all manufacturers. Our analysis suggests that price–volume agreements with a rebate rate of 100% are not likely to be optimal if payers have the ability to negotiate prices as part of the agreement.
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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 | 0.011 | 0.030 |
| Meta-epidemiology (narrow) | 0.001 | 0.002 |
| Meta-epidemiology (broad) | 0.002 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.003 | 0.005 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.003 | 0.002 |
| Insufficient payload (model declined to judge) | 0.004 | 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".