Equilibration of Coordinating Imitation and Best-Response Dynamics
Bibliographic record
Abstract
Decision-making individuals are often considered to be either imitators who copy the action of their most successful neighbors or best-responders who maximize their benefit against the current actions of their neighbors. In the context of coordination games, where neighboring individuals earn more if they take the same action, by means of potential functions, it was shown that populations of all imitators and populations of all best-responders equilibrate in finite time when they become active to update their decisions sequentially. However, for mixed populations of the two, the equilibration was shown only for specific activation sequences. It is therefore, unknown, whether a potential function also exists for mixed populations or if there actually exists a counter example where an activation sequence prevents equilibration. We show that in a linear graph, the number of “sections” (a sequence of consecutive individuals taking the same action) serves as a potential function, leading to equilibration, and that this result can be extended to sparse trees. The existence of a potential function for other types of networks remains an open problem.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.010 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.006 | 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), 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".