Chaos and unpredictability in evolution of cooperation in continuous time

Taekho You, Minji Kwon, Hang-Hyun Jo*, Woo-Sung Jung, Seung Ki Baek

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

6 Citations (Scopus)
131 Downloads (Pure)

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

Original languageEnglish
Article number062310
Pages (from-to)1-18
Number of pages8
JournalPhysical Review E
Volume96
Issue number6
DOIs
Publication statusPublished - 15 Dec 2017
MoE publication typeA1 Journal article-refereed

Keywords

  • TIT-FOR-TAT
  • PRISONERS-DILEMMA
  • LOSE-SHIFT
  • WIN-STAY
  • CONTINGENCY
  • ADAPTATION
  • EXTINCTION
  • DEFECTION
  • SELECTION
  • SUICIDE

Cite this