Competitive pricing for spectrum subleasing for future wireless ad hoc networks
Bibliographic record
Abstract
This paper envisions a near future in which the proliferation of wireless ad hoc networks in urban centers causes excessive spectrum pollution on currently allocated unlicensed bands. One solution for this problem is for the operators to lease freshly released spectrum from the regulators and sublease it to agencies in major cities. We consider one such operator who divides an urban area into regions and subleases spectrum with the condition that the interference measured at boundary points should not exceed a threshold. The subleasing pricing structure has a fixed part, as well as a variable part that discounts the price based on the margin between the interference threshold and the actual interference. The slope of the variable part is called the discount rate and is determined by a competition that is modeled as a game within a game. For a fixed discount rate, the competition between the customers forms a strategic game. The end result of this game becomes the input to the Stackelberg game between the customers as a whole on the one side and the operator on the other side. We derive the mild condition under which the strategic game of the customers has a unique Nash equilibrium, and obtain an explicit closed form solution for the equilibrium point. This result is then used to derive the best response of the operator and the optimum (Stackelberg equilibrium) discount rate the operator would want to offer. Numerical results obtained through simulations that support the analysis are also provided.
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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 | 0.002 | 0.007 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| 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) | 0.004 | 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".