An equilibrium-based framework for managing collusion in multi-channel supply chains
Bibliographic record
Abstract
Collusion among retailers remains a persistent concern in multi-channel supply chains, where competition has intensified with the rise of online platforms and direct manufacturer sales. Despite extensive research on channel coordination and pricing strategies, limited attention has been given to how e-tailers and direct web-store channels influence collusive behavior and welfare outcomes. To address this gap, this study develops a game-theoretic model of a manufacturer-led supply chain comprising a traditional retailer, an e-tailer, and a manufacturer’s direct web-store. We analyze four structural scenarios and three decision-making modes (competition, collusion, and centralized coordination) to derive the equilibrium strategies of all participants. The results show that collusion increases retailers’ joint profits only when no web-store channel exists, but introducing a direct channel weakens the profitability and stability of collusion. Moreover, the welfare effects depend critically on the e-tailer’s contractual design: under the agency format, collusion may enhance coordination and total welfare, while under the reselling format, it raises prices and harms consumers. The study contributes to the emerging literature on anti-collusion mechanisms in digital supply chains, offering analytical insights and managerial guidance for manufacturers, retailers, and regulators seeking to manage competition and fairness in multi-channel environments.
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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 | 0.011 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.002 | 0.004 |
| Scholarly communication | 0.004 | 0.006 |
| Open science | 0.004 | 0.004 |
| Research integrity | 0.004 | 0.003 |
| Insufficient payload (model declined to judge) | 0.010 | 0.001 |
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".