Pricing optimization and competition under the linear nested stochastic choice model
Bibliographic record
Abstract
Abstract In this article, we investigate the pricing optimization of firms selling multiple alternatives to the market where consumer purchase behavior follows the linear nested stochastic choice (LNSC) model. As a special case of the nested stochastic choice (NSC) model, LNSC similarly features a two‐step Luce procedure. Considering differentiated price sensitivities in a non‐exact preference function form, the present research specifically shows that, for any product in each nest, the adjusted markup is constant under certain conditions; and the adjusted nest‐level markup is constant among nests under another sufficient condition. The “loss‐leader” effect is observed, which indicates that it may be optimal to price a product with a negative adjusted markup or even a negative margin to attract more attention to the corresponding nest. Based on these results, the pricing optimization can be simplified to a single‐variable problem where the objective function is unimodal. Then, a special case with an exponential preference function is discussed along with its concavity of the total expected profit. The above results are also used to construct the oligopoly multiproduct price competition and characterize the Nash equilibrium. Finally, a series of sensitivity analyses are conducted to reveal the impacts of key parameters on the optimal solutions.
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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 | 0.009 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.002 | 0.002 |
| Insufficient payload (model declined to judge) | 0.005 | 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".