Sample path analysis of contribution and reward in cooperative groups

Hiroshi Toyoizumi*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)


Explaining cooperative behavior is one of the major challenges in both biology and human society. The individual reward in cooperative group depends on how we share the rewards in the group. Thus, the group size dynamics in a cooperative group and reward-allocation rule seem essential to evaluate the emergence of cooperative groups. We apply a sample path-based analysis called an extension of Little's formula to general cooperative group. We show that the expected reward is insensitive to the specific reward-allocation rule and probabilistic structure of group dynamics, and the simple productivity condition guarantees the expected reward to be larger than the average contribution. As an example, we take social queues to see the insensitivity result in detail.

Original languageEnglish
Pages (from-to)311-314
Number of pages4
JournalJournal of Theoretical Biology
Issue number3
Publication statusPublished - 2009 Feb 7
Externally publishedYes


  • Altruism
  • Cooperation
  • Little's formula
  • Queueing theory
  • Social queue

ASJC Scopus subject areas

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


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