Nash Equilibrium Seeking with Dynamic Agents in Networks
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Bibliographic record
Abstract
In this thesis, we investigate methods of designing distributed (generalized) Nash equilibrium (GNE) seeking algorithms in continuous-time for agents with inherent dynamics. In real-world applications, the action of each agent may correspond to a physical quantity, that is actuated through a control input. In such settings, the algorithms considered take the form of distributed, dynamic feedback controllers with networked communication that seek to drive the action to the (G)NE in steady-state. The specific contributions of the thesis take two forms. First, we propose a general framework for designing distributed Nash equilibrium (NE) seeking controllers for decoupled LTI agents. Using this methodology, we show that the problem is reduced to the design of a set of decentralized stabilizing controllers. We investigate various methods of designing these controllers, first for quadratic games using LTI control theory and diagonal stability theory and then for non-quadratic games using passivity and H-infinity control theory. Second, we consider designing distributed GNE seeking feedbacks for dynamic agents in games with coupled constraints. Current methods can only ensure constraint satisfaction in steady-state. In contrast, we propose an inexact penalty method using a barrier function for agents with equilibrium-independent passive dynamics. Initially, we show that with fixed barrier function these dynamics converge to a suboptimal epsilon-GNE while satisfying the constraints for all time, not only in steady-state. Then, we consider allowing the log-barrier function to vary in time in order to achieve exact convergence to the variational GNE.
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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 | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.001 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.001 | 0.002 |
| 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