Optimal Bayesian Demand Learning over Short Horizons
Why this work is in the frame
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Bibliographic record
Abstract
We investigate the optimal Bayesian dynamic pricing and demand learning policy over short selling horizons, where the pricing decisions are time‐sensitive. The seller fine‐tunes the price near an incumbent price in order to maximize the total revenue. The existing literature focuses on policies that are asymptotically optimal, that is, near optimal when the selling horizons are sufficiently long, but little is known about the optimal Bayesian policies, especially over short horizons. We formulate the problem as a finite‐horizon stochastic dynamic program and identify a connection between the optimality equations and the generalized Weierstrass transform (GWT). We fully characterize the structure of the Bayesian optimal policy for the linear Gaussian demand model and prove that the optimal policy adjusts the myopic price away from the incumbent price. A notable exception occurs when the two prices coincide and the precision of the posterior belief exceeds a threshold, in which case it is optimal to forgo learning and use a fixed‐price policy. Exploiting the structural results makes it possible to compute the optimal policy efficiently on an ordinary computer.
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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 | 0.001 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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 it