Diffusion and pattern formation in spatial games
Bibliographic record
Abstract
Diffusion plays an important role in a wide variety of phenomena, from bacterial quorum sensing to the dynamics of traffic flow. While it generally tends to level out gradients and inhomogeneities, diffusion has nonetheless been shown to promote pattern formation in certain classes of systems. Formation of stable structures often serves as a key factor in promoting the emergence and persistence of cooperative behavior in otherwise competitive environments, however, an in-depth analysis on the impact of diffusion on such systems is lacking. We therefore investigate the effects of diffusion on cooperative behavior using a cellular automaton (CA) model of the noisy spatial iterated prisoner's dilemma (IPD), physical extension, and stochasticity being unavoidable characteristics of several natural phenomena. We further derive a mean-field (MF) model that captures the three-species predation dynamics from the CA model and highlight how pattern formation arises in this new model, then characterize how including diffusion by interchange similarly enables the emergence of large scale structures in the CA model as well. We investigate how these emerging patterns favors cooperative behavior for parameter space regions where IPD error rates classically forbid such dynamics. We thus demonstrate how the coupling of diffusion with nonlinear dynamics can, counterintuitively, promote large-scale structure formation and in return establish new grounds for cooperation to take hold in stochastic spatial systems.
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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 | 0.004 |
| 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 | 0.003 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 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 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".