Dynamic Nash Equilibrium Seeking for Higher-Order Integrators in Networks
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Bibliographic record
Abstract
In this paper we consider a set of heterogeneous agents modelled as higher-order integrators, playing a game over a network. In such networked scenarios, agents have to make decisions compatible with seeking a Nash equilibrium, while using partial-networked information, and possibly rejecting disturbances. We propose dynamic agent decision-making based on gradient-play with an additional stabilizing component for the higher-order dynamics. In the partial-information setting, each agent makes its decision based on a dynamic estimate of the others' states, updated by local communication with its neighbours, which offsets the lack of global information. When external disturbances are present, the agent decision dynamics is augmented with an internal-model component, in the form of a reduced-order observer for the disturbance. We show convergence of agents' dynamics to the Nash equilibrium, irrespective of disturbances. Our proofs leverage input-to-state stability under strong monotonicity of the pseudo-gradient and Lipschitz continuity of extended pseudo-gradient. Applications to mobile robots in sensor networks are provided.
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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 | 0.000 | 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 | 0.001 |
| Open science | 0.001 | 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 it