On linear quadratic potential games
Bibliographic record
Abstract
Our paper addresses characterizing conditions for linear quadratic (LQ) games to be potential. The desired properties of potential games in finite action settings, such as convergence of learning dynamics to Nash equilibria and challenges of learning Nash equilibria in continuous state and action settings, motivate us to characterize LQ potential games. Our first contribution is to consider two-player LQ games with full-state feedback and scalar states and action space, and to analytically verify that the set of potential games within this example is limited, essentially differing only slightly from an identical interest game. Given this finding, we restrict the class of LQ games to those with decoupled dynamics and decoupled state linear feedback information structure. For this subclass, we show that the set of potential games strictly includes non-identical interest games and characterize conditions for LQ games in this subclass to be potential. We further derive their corresponding potential function and prove the existence of a Nash equilibrium. Meanwhile, we highlight the challenges in characterizations of the Nash equilibrium for this class of potential LQ games, theoretically and through simulation.
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How this classification was reachedexpand
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 | 0.002 |
| 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 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.001 | 0.006 |
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; both teacher heads agree on what is shown here.
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".