Heterogeneous Mixed Populations of Best-Responders and Imitators: Equilibrium Convergence and Stability
Bibliographic record
Abstract
In anticoordination social contexts such as stock selection, resource allocation, and crowd dispersion, an individual earns more if the opponents adopt her opposite strategy. Based on their experience and available information, individuals may either evaluate all available options and decide on the most profitable one, or simply mimic successful others. These two types of decision-makers are known as best-responders and imitators, respectively. Previous studies have shown that in anticoordination social contexts, a population of best-responders reaches an equilibrium state, where every individual is satisfied with her decision, but a population of imitators is quite likely to never settle and undergo perpetual fluctuations. Most real-world populations, however, consist of both types of individuals, and it remains an open problem whether such mixed-populations eventually reach an equilibrium state. We provide a sharp, yet simple answer to this question: the population almost surely reaches an equilibrium if and only if it admits one. More specifically, we study a well-mixed population of both best-responders and imitators playing anticoordination games with two available strategies, cooperation and defection, and earning according to payoff matrices that can be unique to each player, resulting in a heterogeneous population. The individuals update their strategies asynchronously accordingly to their types: best-responders choose the strategy that maximizes their payoffs against the population and imitators copy the strategy of the individual earning the highest payoff. We find the necessary and sufficient condition for the population dynamics to admit an equilibrium, identify all possible equilibria, investigate their stability and perform convergence analysis.
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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 | 0.002 | 0.014 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.002 | 0.003 |
| Research integrity | 0.002 | 0.001 |
| Insufficient payload (model declined to judge) | 0.004 | 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".