Frequency Loyalty Programs in an Asymmetric Duopoly Market: Theoretical and Empirical Investigations
Bibliographic record
Abstract
This paper examines frequency loyalty programs in an asymmetric duopoly market where one firm has more service locations than the other. We have analyzed the empirical data from a quasi-field experiment in a duopoly gasoline market where the larger firm initially started a full-scale loyalty program but later switched to a partial-scale loyalty program. We found that the larger firm’s loyalty program significantly increased that firm’s market share in the regular gasoline market more than in the premium gasoline market. The equilibrium analysis of a game theoretical model reveals that the optimal scale of a firm’s loyalty program shall increase with the firm’s profit margin as well as the size of the “moving” segment of consumers whose location preferences change over time (i.e., taxi drivers). The theoretical results are consistent with the empirical findings because the regular gasoline market had a sufficiently large “moving” segment while the premium gasoline market did not. Moreover, the larger firm switched from a full-scale loyalty program to a partial-scale program when both the gasoline consumption by taxi drivers as a percentage of total sales and the profit margins of the regular gasoline decreased over time.
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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 | 0.003 | 0.013 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.007 | 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".