Decentralized Learning in Stochastic Games with Local Information
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Bibliographic record
Abstract
In the context of multi-agent systems with decentralized information structures, we study rigorously justified convergence results and associated learning algorithms that converge to equilibria. With this objective in mind, we first review classical equilibrium results, focusing on finite-player games with pure or mixed strategy sets. Results such as Kakutani’s fixed-point theorem and Sion’s minimax theorem establish existence under relatively broad conditions. Building on this background, we then study learning dynamics, including best and better response processes, in which players periodically revise and update strategies to optimize payoffs relative to their previous actions via a policy revision process. This induces a graph on the set of policies which facilitate our mathematical approach which combines graph theory, game theory, stochastic control, and Markov processes. While learning using best/better response dynamics converges under certain conditions reported in Arslan et.al, a new approach to policy revision, termed as satisficing (which may be viewed as a win-stay, lose-shift algorithm), introduced by Yongacoglu et.al provides a strictly richer graph network structure and is applicable to a much broader class of games. In particular, these generalize weakly acyclic games. The question we studied is to precisely characterize the set of games for which such a satisficing process ensures convergence to equilibrium. In particular, we addressed an open question raised by Yongacoglu et al. on necessary and sufficient conditions for convergence to equilibria from any initial policy profile. On sufficiency, we presented a generalization, relaxing requirements to allow multiple pure Nash equilibria, provided at least one is strict and subgame-unique. Our research also presented a nontrivial example of a game that admits a strict pure Nash equilibrium in each induced subgame that fails to converge via satisficing paths, showing that such conditions are insufficient, thus also leading to a necessity condition.
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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) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.003 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| 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