Chaos and unpredictability in evolution of cooperation in continuous time

Research output: Contribution to journalArticleScientificpeer-review

Researchers

Research units

  • Pohang University of Science and Technology
  • Asia Pacific Center for Theoretical Physics
  • Pukyong National University

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

Details

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

    Research areas

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

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