Chaos and unpredictability in evolution of cooperation in continuous time

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Chaos and unpredictability in evolution of cooperation in continuous time. / You, Taekho; Kwon, Minji; Jo, Hang-Hyun; Jung, Woo-Sung; Baek, Seung Ki.

In: Physical Review E, Vol. 96, No. 6, 062310, 15.12.2017, p. 1-18.

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You, Taekho ; Kwon, Minji ; Jo, Hang-Hyun ; Jung, Woo-Sung ; Baek, Seung Ki. / Chaos and unpredictability in evolution of cooperation in continuous time. In: Physical Review E. 2017 ; Vol. 96, No. 6. pp. 1-18.

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@article{ceaff53b63334c6fbc579cc645f77f3b,
title = "Chaos and unpredictability in evolution of cooperation in continuous time",
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 mu",
keywords = "TIT-FOR-TAT, PRISONERS-DILEMMA, LOSE-SHIFT, WIN-STAY, CONTINGENCY, ADAPTATION, EXTINCTION, DEFECTION, SELECTION, SUICIDE",
author = "Taekho You and Minji Kwon and Hang-Hyun Jo and Woo-Sung Jung and Baek, {Seung Ki}",
year = "2017",
month = "12",
day = "15",
doi = "10.1103/PhysRevE.96.062310",
language = "English",
volume = "96",
pages = "1--18",
journal = "Physical Review E",
issn = "2470-0045",
publisher = "American Physical Society",
number = "6",

}

RIS - Download

TY - JOUR

T1 - Chaos and unpredictability in evolution of cooperation in continuous time

AU - You, Taekho

AU - Kwon, Minji

AU - Jo, Hang-Hyun

AU - Jung, Woo-Sung

AU - Baek, Seung Ki

PY - 2017/12/15

Y1 - 2017/12/15

N2 - 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 mu

AB - 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 mu

KW - TIT-FOR-TAT

KW - PRISONERS-DILEMMA

KW - LOSE-SHIFT

KW - WIN-STAY

KW - CONTINGENCY

KW - ADAPTATION

KW - EXTINCTION

KW - DEFECTION

KW - SELECTION

KW - SUICIDE

U2 - 10.1103/PhysRevE.96.062310

DO - 10.1103/PhysRevE.96.062310

M3 - Article

VL - 96

SP - 1

EP - 18

JO - Physical Review E

JF - Physical Review E

SN - 2470-0045

IS - 6

M1 - 062310

ER -

ID: 16828420