Repeated Game Analysis for Cooperative MAC With Incentive Design for Wireless Networks
Bibliographic record
Abstract
Cooperative communications offer appealing potentials to improve quality of service (QoS) for wireless networks. Many existing works on cooperative communications assume that participation in cooperative relaying is unconditional. In practice, however, due to resource consumption, it is vital to provide incentives for selfish cooperating peer nodes. In this paper, we analyze a cooperative medium access control (MAC) protocol with incentive design using a game-theoretic approach. Specifically, our analysis addresses two questions: 1) Can a cooperating agreement be reached between peer nodes, and 2) can cooperating lead to higher utility than not cooperating? We first formulate a one-stage game for the slotted-Aloha-based cooperative MAC protocol, where not cooperating is a Nash equilibrium (NE) strategy, whereas cooperating is not. To exploit cooperation gain, the one-stage game is extended to a two-stage game by incorporating an incentive mechanism that adapts channel access probabilities with tuning factors. Based on the Markov chain analysis of the system states with the repeated two-stage games, we determine valid tuning factors, guaranteeing that cooperating attains an NE and provides expected utility not less than that of the not-cooperating NE. Moreover, a special case with saturated and symmetric assumptions is investigated, and closed-form criteria for the tuning factors are derived. Finally, we compare the derived tuning factors for individual nodes with an optimal choice that is selected from the system perspective to maximize the overall system utility. The numerical results confirm our analytical conclusions and demonstrate that the tuning factors selected according to our derived criteria can achieve high utility that is slightly lower than that of the optimal choice.
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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 | 0.004 | 0.011 |
| Meta-epidemiology (narrow) | 0.002 | 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 | 0.002 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.002 | 0.003 |
| 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".