Chaos and unpredictability in evolution of cooperation in continuous time
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Volume Title
A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä
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Date
2017-12-15
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Mcode
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Language
en
Pages
8
1-18
1-18
Series
PHYSICAL REVIEW E, Volume 96, issue 6
Abstract
Cooperators benefit others with paying costs. Evolution of cooperation crucially depends on the cost-benefit ratio of cooperation, denoted as c. In thiswork, 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 muDescription
Keywords
TIT-FOR-TAT, PRISONERS-DILEMMA, LOSE-SHIFT, WIN-STAY, CONTINGENCY, ADAPTATION, EXTINCTION, DEFECTION, SELECTION, SUICIDE
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Citation
You, T, Kwon, M, Jo, H-H, Jung, W-S & Baek, S K 2017, ' Chaos and unpredictability in evolution of cooperation in continuous time ', Physical Review E, vol. 96, no. 6, 062310, pp. 1-18 . https://doi.org/10.1103/PhysRevE.96.062310
