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Generalized Social Dilemmas: The Evolution of Cooperation in Populations with Variable Group Size

Broom, M. ORCID: 0000-0002-1698-5495, Pattni, K. & Rychtar, J. (2018). Generalized Social Dilemmas: The Evolution of Cooperation in Populations with Variable Group Size. Bulletin of Mathematical Biology, 81(11), pp. 4643-4674. doi: 10.1007/s11538-018-00545-1


Evolutionary game theory is an important tool to model animal and human behaviour. A key class of games are the social dilemmas, where cooperation benefits the group but defection benefits the individual within any group. Previous works have considered which games qualify as social dilemmas, and different categories of dilemmas, but have generally concentrated on fixed sizes of interacting groups. In this paper we develop a systematic investigation of social dilemmas on all group sizes. This allows for a richer definition of social dilemmas. For example, while increasing a group size to include another defector is always bad for all existing group members, extra cooperators can be good or bad, depending upon the particular dilemma and group size. We consider a number of commonly used social dilemmas in this context, and in particular show the effect of variability in group sizes for the example of a population comprising negative binomially distributed group sizes. The most striking effect is that increasing the variability in group sizes for non-threshold public goods games is favourable for the evolution of cooperation. The situation for threshold public goods games and commons dilemmas is more complex.

Publication Type: Article
Additional Information: © The Author(s) 2018. This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (, which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
Publisher Keywords: Evolutionary game, Cooperation, Public goods game, Prisoner’s Dilemma, Hawk–Dove game
Subjects: H Social Sciences > HM Sociology
Q Science > QA Mathematics
Departments: Bayes Business School > Management
SWORD Depositor:
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