Heterogeneity, reinforcement learning, and chaos in population games
Bibliographic record
Abstract
Inspired by the challenges at the intersection of Evolutionary Game Theory and Machine Learning, we investigate a class of discrete-time multiagent reinforcement learning (MARL) dynamics in population/nonatomic congestion games, where agents have diverse beliefs and learn at different rates. These congestion games, a well-studied class of potential games, are characterized by individual agents having negligible effects on system performance, strongly aligned incentives, and well-understood advantageous properties of Nash equilibria. Despite the presence of static Nash equilibria, we demonstrate that MARL dynamics with heterogeneous learning rates can deviate from these equilibria, exhibiting instability and even chaotic behavior and resulting in increased social costs. Remarkably, even within these chaotic regimes, we show that the time-averaged macroscopic behavior converges to exact Nash equilibria, thus linking the microscopic dynamic complexity with traditional equilibrium concepts. By employing dynamical systems techniques, we analyze the interaction between individual-level adaptation and population-level outcomes, paving the way for studying heterogeneous learning dynamics in discrete time across more complex game scenarios.
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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 | 0.002 | 0.001 |
| 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 | 0.001 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, 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".