Optimal Investment Decisions for Two Positioned Firms Competing in a Duopoly Market with Hidden Competitors
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Bibliographic record
Abstract
Abstract This paper extends the literature dealing with the option to invest in a duopoly market for a leader‐follower setting. A restrictive assumption embodied in the models in the current literature is that investment opportunities are semi‐proprietary in that the two identified or positioned firms are guaranteed to hold at least the follower's position. More competition is realistically captured in our model by introducing the concept of hidden rivals so that the places in the market can be taken not only by positioned firm but also by these hidden competitors. The value functions and the optimal triggers for the positioned firms differ materially in settings with(out) the presence of hidden rivals. Unlike existing models, our model allows for (a)symmetric market shares and investment costs for the leader and the follower. Cooperative entrance by the two positioned firms is also modelled.
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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 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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