2017/12/15 by Taekho You, Minji Kwon, Hang-Hyun Jo +3 · 1 citation
Biochemistry, Genetics and Molecular Biology · Mathematics · Medicine · Physics and Astronomy · Social Sciences · #Artificial intelligence #Bifurcation #Biology #Chaotic #Computer science #Demography #Evolution and Genetic Dynamics #Evolutionary Game Theory and Cooperation #Evolutionary dynamics #Genetics #Logistic map #Mathematical and Theoretical Epidemiology and Ecology Models #Mathematical economics #Mathematics #Mutation #Mutation rate #Nonlinear system #Physics #Population #Quantum mechanics #Randomness #Replicator equation #Sequence (biology) #Sociology #Statistical physics #Statistics #nlin.CD #q-bio.PE
paper · pdf · doi:10.1103/physreve.96.062310
9 pages; 3 figures
openalex publication_date 2017/12/15 · arxiv created 2017/12/16 · arxiv updated 2017/12/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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 μ≪1, the position of the bifurcation sequence on the c axis is numerically found to scale as μ0.1, and such sensitivity to μ suggests that mutation may have nonperturbative effects on evolutionary paths. It demonstrates how the microscopic randomness of the mutation process can be amplified to macroscopic unpredictability by evolutionary dynamics.