A Passivity-Based Approach to Nash Equilibrium Seeking Over Networks
Bibliographic record
Abstract
In this paper, we consider the problem of distributed Nash equilibrium (NE) seeking over networks, a setting in which players have limited local information on the others' decisions. We start from a continuous-time gradient-play dynamics that converges to an NE under strict monotonicity of the pseudogradient and assumes perfect information. We consider how to modify it in the case of partial, or networked information between players. We propose an augmented gradient-play dynamics with correction, in which players communicate locally only with their neighbors to compute an estimate of the other players' actions. We derive the new dynamics based on the reformulation as a multiagent coordination problem over an undirected graph. We exploit incremental passivity properties and show that a synchronizing, distributed Laplacian feedback can be designed using relative estimates of the neighbors. Under a strict monotonicity property of the pseudogradient, we show that the augmented gradient-play dynamics converges to consensus on the NE of the game. We further discuss two cases that highlight the tradeoff between properties of the game and the communication graph.
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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 | 0.006 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.002 | 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".