Optimal Price Competition for Spectrum Sharing in Cognitive Radio: A Dynamic Game-Theoretic Approach
Bibliographic record
Abstract
Optimal pricing for dynamic spectrum sharing in "cognitive radio" networks is an open research issue. In this paper, we address the problem of spectrum pricing in a cognitive radio environment in which multiple primary services with spectrum opportunity compete with each other to offer spectrum access to the secondary services. By using an optimal pricing scheme, each of the primary services aims to maximize its profit under quality of service (QoS) constraint. We formulate this situation as an oligopoly market consisting of a few firms and a consumer. For a primary service/user, the QoS degradation is considered as the cost incurred for offering spectrum access to the secondary service/user. For the secondary service, we adopt a utility function to obtain the demand function. With a <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Bertrand</i> <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">game</i> model, we are able to analyze the impacts of several system parameters such as spectrum substitutability and channel quality on the Nash equilibrium (i.e., optimal pricing adopted by the primary services). In addition, we present distributed iterative game algorithms to obtain the solution. The stability of the proposed iterative game algorithms in terms of convergence to the Nash equilibrium is studied.
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How this classification was reachedexpand
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 | 0.001 |
| 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, 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".