Loyalty Rewards Facilitate Tacit Collusion
Why this work is in the frame
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Bibliographic record
Abstract
Using a dynamic overlapping‐generations model, we show that loyalty rewards robustly facilitate tacit collusion. We compare the sustainability of tacit collusion when uniform prices are used, when loyal customers are rewarded without using commitment, and when loyalty rewards are implemented by committing to offering customers either lower fixed repeat‐purchase prices or fixed repeat‐purchase discounts. We find that, relative to uniform prices, rewarding loyalty without using commitment on the equilibrium path makes tacit collusion easier to sustain, because a deviating firm is unable to steal one period of industry profit before losing all future profits. When loyalty rewards are offered by firms committing to repeat‐purchase prices, collusion is even easier to sustain, because a deviating firm cannot renege on its discounted price for repeat‐purchase customers. When firms commit to repeat‐purchase discounts, they also commit to lowering the price for their repeat‐purchase customers if they undercut the regular price, rendering tacit collusion to be even more readily sustainable. Our results hold whether products are homogeneous or horizontally differentiated as in a Hotelling model.
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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 | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.001 | 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 it