A simple rule for the evolution of contingent cooperation in large groups

Roberto H. Schonmann, Robert Boyd

Research output: Contribution to journalArticlepeer-review

14 Scopus citations


Humans cooperate in large groups of unrelated individuals, and many authors have argued that such cooperation is sustained by contingent reward and punishment. However, such sanctioning systems can also stabilize a wide range of behaviours, including mutually deleterious behaviours. Moreover, it is very likely that large-scale cooperation is derived in the human lineage. Thus, understanding the evolution of mutually beneficial cooperative behavior requires knowledge of when strategies that support such behaviour can increasewhen rare. Here,we derive a simple formula that gives the relatedness necessary for contingent cooperation in n-person iterated games to increase when rare. This rule applies to a wide range of pay-off functions and assumes that the strategies supporting cooperation are based on the presence of a threshold fraction of cooperators. This rule suggests that modest levels of relatedness are sufficient for invasion by strategies that make cooperation contingent on previous cooperation by a small fraction of group members. In contrast, only high levels of relatedness allow the invasion by strategies that require near universal cooperation. In order to derive this formula, we introduce a novel methodology for studying evolution in group structured populations including local and global group-size regulation and fluctuations in group size.

Original languageEnglish (US)
JournalPhilosophical Transactions of the Royal Society B: Biological Sciences
Issue number1687
StatePublished - Feb 5 2016


  • Contingent punishment
  • Cooperation
  • N-person reciprocity
  • Relatedness

ASJC Scopus subject areas

  • General Biochemistry, Genetics and Molecular Biology
  • General Agricultural and Biological Sciences


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