Newsvendors Under Simultaneous Price and Inventory Competition
Bibliographic record
Abstract
This paper extends the theory of N competitive newsvendors to the case where competition occurs simultaneously in price and inventory. The basic research questions are whether the Nash equilibrium exists in this game, whether it is unique, and how the resulting inventories and prices are affected by competition. Using a novel method, we show the quasiconcavity of the competitive newsvendor's problem and establish the existence of the pure-strategy Nash equilibrium. Through a contraction mapping approach, we develop sufficient conditions for the Nash equilibrium to be unique. We then analyze the properties of the equilibrium and compare it with the optimal solution for the (noncompeting) price-sensitive newsvendor. We prove that at a symmetric equilibrium, retail prices and safety stocks strictly increase with the proportion of a newsvendor's unsatisfied customers that switch to a competitor, but strictly decrease with the intensity of price competition. Total inventories, on the other hand, increase with the intensity of price competition. Furthermore, the competitive equilibrium never has lower safety stocks and higher retail prices (a situation that definitely hurts the customers) than the solution for noncompetitive newsvendors.
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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 | 0.003 | 0.009 |
| 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 | 0.002 | 0.004 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.002 | 0.001 |
| Insufficient payload (model declined to judge) | 0.004 | 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".