Cheat-Proof Distributed Power Control in Full-Duplex Small Cell Networks: A Repeated Game With Imperfect Public Monitoring
Bibliographic record
Abstract
We address the problem of distributed power control in a two-tier cellular network, where full-duplex small cells underlay a macro cell in a co-channel deployment scenario. We first formulate the distributed power control problem as a non-cooperative game and then extend it to a repeated game with imperfect public monitoring. The repeated game formulation prevents deceitful small cells from deviating from the social optimal solution for their own benefit. We establish the existence and uniqueness of the Nash equilibrium in the formulated non-cooperative game. We also characterize the set of public perfect equilibrium for the repeated game. A two-phase distributed algorithm is proposed to achieve and enforce a Pareto optimal transmit power profile. The solution obtained by this algorithm is also social optimal. Phase 1 of the algorithm is a fully distributed learning phase based on perturbed Markov chains, where each base station individually learns a Pareto optimal operating point. Phase 2 is composed of two rules: 1) a detection rule based on Page-Hinckley test to detect cheating and 2) a punishment rule to motivate cheating base stations to cooperate. Through theoretical analysis, we prove that the proposed distributed power control mechanism achieves a public perfect equilibrium point of the formulated repeated game. The power control algorithm is also cheat-proof and needs only a small amount of information exchange among network nodes. The effectiveness of the algorithm is shown through numerical analysis. Our proposed model, algorithm, and analysis are also valid for a half-duplex system as a special case.
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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 | 0.005 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.002 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| 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 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".