System-wide incentives to trace food processing: A cooperative-game analysis
Bibliographic record
Abstract
This paper uses cooperative game theory to analyze the incentives for firms to adopt product tracing in a three-tier food processing system with multiple farmers, one manufacturer, and one retailer. Firms that adopt the tracing system can either form a single coalition or create multiple coalitions, while non-adopters make decisions independently. Our analysis identifies equilibrium outcomes for all possible coalition structures, showing that collaboration between the manufacturer and retailer boosts system-wide efficiency, and fewer coalitions lead to greater overall benefits. We develop a coalition game in characteristic value form and prove that the game’s core is always non-empty. The Center of Gravity of the Imputation Set-based value (CIS-value) is a core element of our game and it matches the nucleolus when the system includes at least three farmers. However, the CIS-value does not always ensure non-negative allocations for all coalition members. To resolve this, we introduce the Evenly-Split Value (ES-value), which stays within the core and guarantees positive allocations for every member of the tracing coalition.
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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 | 0.004 | 0.009 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.002 | 0.004 |
| Open science | 0.002 | 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".