Model-Free Assortment Pricing with Transaction Data
Bibliographic record
Abstract
We study the problem when a firm sets prices for products based on the transaction data, that is, which product past customers chose from an assortment and what were the historical prices that they observed. Our approach does not impose a model on the distribution of the customers’ valuations and only assumes, instead, that purchase choices satisfy incentive-compatible constraints. The uncertainty set of potential valuations of each past customer can then be encoded as a polyhedral set, and our approach maximizes the worst case revenue, assuming that new customers’ valuations are drawn from the empirical distribution implied by the collection of such polyhedra. We study the single-product case analytically and relate it to the traditional model-based approach. Then, we show that the optimal prices in the general case can be approximated at any arbitrary precision by solving a compact mixed-integer linear program. We further design three approximation strategies that are of low computational complexity and interpretable. In particular, the cutoff pricing heuristic has a competent provable performance guarantee. Comprehensive numerical studies based on synthetic and real data suggest that our pricing approach is uniquely beneficial when the historical data has a limited size or is susceptible to model misspecification. This paper was accepted by Omar Besbes, revenue management and market analytics. Funding: This work was supported by the Rotman School of Management (TD-MDAL Research Grant) and the Natural Sciences and Engineering Research Council of Canada [Grants RGPIN-2015-06757, RGPIN-2020-04038, RGPIN-2020-06054, RGPIN-2021-04295]. Supplemental Material: The e-companion and data files are available at https://doi.org/10.1287/mnsc.2022.4651 .
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.002 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.004 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.001 | 0.004 |
| Open science | 0.003 | 0.002 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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 teacher head, 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".