Dynamic Pricing with a Poisson Bandit Model
Why this work is in the frame
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Bibliographic record
Abstract
Abstract Suppose that one of two prices for the same product must be posted every day. Under each price, the demand function is described by a compound Poisson process with possibly unknown parameters. The objective is to sequentially post daily prices so as to maximize the total expected, possibly discounted gross revenue over a finite pricing horizon. To effectively balance between understanding the demand function and achieving economic revenues, we formulate the optimal pricing problem with a bandit model and characterize the solution by means of stochastic dynamic programming. When there is only one unknown demand function in the model, the optimal pricing decision is determined by a pricing index, whose limit is the Gittins index. These index values also demonstrate that it may be worth sacrificing some immediate payoff for the benefit of information gathering and better-informed decisions in the future. Moreover, the optimal stopping solution is derived and the myopic strategy is shown not to be optimal in general. When both demand functions are unknown, a version of the play-the-winner pricing rule is derived.
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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 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.000 | 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