Graphon Mean Field Games and the GMFG Equations
Why this work is in the frame
A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.
Bibliographic record
Abstract
Networks are ubiquitous in modern society and the need to analyse, design and control them is evident. However many technical and social networks apparently grow unboundedly over time. This has the undesirable consequence that, inevitably, any method founded upon techniques whose effectiveness decreases with the size of the network will eventually be overwhelmed. This paper presents a framework called Graphon Mean Field Game (GMFG) theory for the analysis and control of non-cooperative dynamical game systems distributed over networks of unbounded size. This work is based upon the recently developed and profoundly influential graphon theory of large networks and their infinite limits. A theory for the centralized control of asymptotically infinite networks has already been formulated within the framework of dynamical systems on graphons [Gao and Caines, CDC 2017]. The current work greatly extends that analysis to populations of competing dynamical agents for which the game theoretic equilibria are expressed in terms of the newly defined Graphon Mean Field (GMFG) equations, these being a significant generalization of the classical MFG PDEs. Furthermore, in this paper, existence and uniqueness theorems for GMFG equations are given together with a sketch of the corresponding epsilon-Nash theory for GMFG systems.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.002 | 0.001 |
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