تقرير
Chaos and unpredictability in evolution of cooperation in continuous time
| العنوان: | Chaos and unpredictability in evolution of cooperation in continuous time |
|---|---|
| المؤلفون: | You, Taekho, Kwon, Minji, Jo, Hang-Hyun, Jung, Woo-Sung, Baek, Seung Ki |
| سنة النشر: | 2017 |
| المجموعة: | Nonlinear Sciences Quantitative Biology |
| مصطلحات موضوعية: | Quantitative Biology - Populations and Evolution, Nonlinear Sciences - Chaotic Dynamics |
| الوصف: | Cooperators benefit others with paying costs. Evolution of cooperation crucially depends on the cost-benefit ratio of cooperation, denoted as $c$. In this work, we investigate the infinitely repeated prisoner's dilemma for various values of $c$ with four of the representative memory-one strategies, i.e., unconditional cooperation, unconditional defection, tit-for-tat, and win-stay-lose-shift. We consider replicator dynamics which deterministically describes how the fraction of each strategy evolves over time in an infinite-sized well-mixed population in the presence of implementation error and mutation among the four strategies. Our finding is that this three-dimensional continuous-time dynamics exhibits chaos through a bifurcation sequence similar to that of a logistic map as $c$ varies. If mutation occurs with rate $\mu \ll 1$, the position of the bifurcation sequence on the $c$ axis is numerically found to scale as $\mu^{0.1}$, and such sensitivity to $\mu$ suggests that mutation may have non-perturbative effects on evolutionary paths. It demonstrates how the microscopic randomness of the mutation process can be amplified to macroscopic unpredictability by evolutionary dynamics. Comment: 9 pages; 3 figures |
| نوع الوثيقة: | Working Paper |
| DOI: | 10.1103/PhysRevE.96.062310 |
| URL الوصول: | http://arxiv.org/abs/1712.05906 |
| رقم الأكسشن: | edsarx.1712.05906 |
| قاعدة البيانات: | arXiv |
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