Price and revenue bounds for bundles of information goods
Bibliographic record
Abstract
Abstract In this paper, we investigate the behavior of the expected revenue function generated from selling bundles with arbitrarily many components. A motivating example of such bundles includes the production and delivery of digital content, where variable costs are generally negligible. Specifically, we derive generic lower and upper bounds for the expected revenue function even when accounting for arbitrary, potentially complex, dependence structures among the bundle components. The expected revenue bounds in turn provide upper and lower bounds regarding the optimal pure bundle price. Our results reconcile the extant bundling literature involving expected revenue bounds, while sharpening some of these results even when relaxing the traditional assumption of independence among the valuations for the bundle components. We show how these bounds can be further tightened when the seller has additional information about the dependence relationship. Since these results effectively reduce the search space for the optimal bundle price, the pricing bounds provided by our framework have important managerial implications.
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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 | 0.006 | 0.035 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| 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 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".