Nonsmooth dynamics of generalized Nash games
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
The generalized Nash equilibrium problem (GNEP) is an N-player noncooperative game, where each player has to solve a nonlinear optimization problem whose objective function and constraints depend on the choices of the other players. As in the case of classic Nash games, where other players' choices only impact a player's objective function, a natural question arises as to how players might evolve their strategies over time, and whether or not this evolution would allow them to reach a Nash equilibrium strategy. The approach in classical Nash games is that of introducing some form of differential equations/systems whose stable points are exactly the Nash strategies of the game. This approach leads to considering projected dynamical systems and sweeping processes. In this paper, we show that these dynamical system approaches can be extended to the case of the GNEP. We present dynamical systems that are useful in this context and discuss the new difficulties introduced by this more complex game. Finally, we show how to exploit the existence proof to build numerical methods and solve GNEP problems from the literature.
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 | 0.001 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.002 |
| 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) | 0.001 | 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