A condition for cooperation in a game on complex networks

Tomohiko Konno*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

42 Citations (Scopus)


We study a condition of favoring cooperation in Prisoner's Dilemma game on complex networks. There are two kinds of players: cooperators and defectors. Cooperators pay a benefit b to their neighbors at a cost c, whereas defectors only receive a benefit. The game is a death-birth process with weak selection. Although it has been widely thought that b/c>〈k〉 is a condition of favoring cooperation (Ohtsuki et al., 2006), we find that b/c>〈knn〉 is the condition. We also show that among three representative networks, namely, regular, random, and scale-free, a regular network favors cooperation the most, whereas a scale-free network favors cooperation the least. In an ideal scale-free network, cooperation is never realized. Whether or not the scale-free network and network heterogeneity favor cooperation depends on the details of the game, although it is occasionally believed that these favor cooperation irrespective of the game structure.

Original languageEnglish
Pages (from-to)224-233
Number of pages10
JournalJournal of Theoretical Biology
Issue number1
Publication statusPublished - 2011 Jan 21
Externally publishedYes


  • Analytical solution
  • Cooperation
  • Games
  • Networks
  • Prisoner's Dilemma

ASJC Scopus subject areas

  • Medicine(all)
  • Immunology and Microbiology(all)
  • Biochemistry, Genetics and Molecular Biology(all)
  • Agricultural and Biological Sciences(all)
  • Modelling and Simulation
  • Statistics and Probability
  • Applied Mathematics


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