Strategic advance sales, demand uncertainty and overcommitment
Bibliographic record
Abstract
We study a game in which producers can sell in two periods: one before a random demand is fully revealed and one after. This type of game corresponds to models of strategic forward trading or of advance sales to intermediaries or consumers. Demand variations and committed advance sales results in the possibility that the net residual demand in the final stage may be so low that it is not profitable for producers make additional sales, or indeed, may even drive the final period price to zero, introducing some convexity into producers’ payoffs. If this possibility of ex post overcommitment occurs on the equilibrium path, it reduces the level of advance sales chosen by producers, muting the pro-competitive effects found under deterministic demand. We establish a condition that determines whether or not demand uncertainty is “minor”, in the sense that the equilibrium depends only on the expected value of the demand shock. In addition, we demonstrate that when the support of demand shocks is narrow enough compared to the marginal cost of production, there exists a unique symmetric subgame-perfect equilibrium in pure strategies. When the support of demand shocks is wider, we establish a regularity condition on the distribution of demand shocks and the model parameters that ensures the existence of a unique equilibrium in pure strategies. We illustrate through examples that commonly used uni-modal distributions satisfy this condition, while bi-model distributions may not.
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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 | 0.001 | 0.008 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.002 | 0.002 |
| Insufficient payload (model declined to judge) | 0.004 | 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".