Selling to a cartel of retailers: a model of hub-and-spoke collusion
Bibliographic record
Abstract
This model describes the working of hub-and-spoke collusion that has been discussed recently by competition policy authorities. We develop a model of tacit collusion between a manufacturer and two retailers, competing a la Rotemberg and Saloner (1986). The best collusive equilibrium between retailers is inefficient and it is in the interest of the supplier to help retailers reach a more efficient collusive equilibrium. The hub and spoke conspiracy reduces double marginalization, but raises the ability of retailers to collude. The impact of a hub-and-spoke cartel on consumer's welfare depends on the bargaining power in the relationship. If the supplier has the bargaining power, the agreement, comparable to a vertical restraint, can be welfare improving in reducing double marginalization. When retailers have the bargaining power, the agreement is closer to an horizontal agreement in which retailers use the supplier to improve their collusive scheme, which leads to a loss of welfare. The result has important implications for competition policy and antitrust enforcement which are further developed in our companion paper Sahuguet and Walckiers (2013).
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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 | 0.003 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.002 | 0.003 |
| Scholarly communication | 0.005 | 0.005 |
| Open science | 0.004 | 0.003 |
| Research integrity | 0.007 | 0.003 |
| Insufficient payload (model declined to judge) | 0.024 | 0.003 |
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".