Cooperation can be observed at all levels of biological and social organization. This is puzzling, as simple theoretical models predict that while cooperation is the most beneficial for a group, non-cooperation is always the most successful strategy for the individual. As such a discrepancy exists, it is interesting to identify the conditions that actually give rise to altruism. This has been addressed in game theoretical frameworks with the typical assumption of dyadic interactions, where cooperation may be stabilized via mechanisms such as memory ; reputation  or kin assortment . One extension to dyadic games is the Public Goods Game, where interactions occur among several players. Typically, the size of cooperative groups is assumed constant; however, it has been shown that relaxation of this assumption is of significance to the maintenance of cooperation. In  it was shown that only the physical distribution of group sizes can promote cooperation. However, explicit mechanisms of group formation processes, as well as the evolution and consequences of these, have yet to be explored, which is the objective of this study.
Mathematical formulations of the time development of group-size distributions are used to determine the expected structure of group sizes. The success of individuals with different strategies can be derived via the structure of group sizes. The level of success determines the evolution of the strategies, which is analyzed in the framework of adaptive dynamics.
A general analytical formalization of group formation processes was derived that allows for realistic creation and dissolution of groups, as well as a realistic flow of individuals between groups. From these processes, joint probability distributions of the number of cooperators and non-cooperators in groups were derived. A simplified method of deriving invasion-fitness in structured populations was developed, and was used to calculate the evolutionary trajectories of individuals' group formation traits. This allowed identification of conditions for various configurations of the expected number of cooperators, and non-cooperators, in the population, some of which configurations allow for coexistence between cooperators and defectors or even an immunized cooperative population.
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Henrik Sjödin, of Umeå Universty, Sweden, is a citizen of Sweden and was funded by IIASA's Swedish National Member Organization. He worked in the Evolution and Ecology Program (EEP) during the YSSP, with an emphasis on the evolutionary ecology of dispersal.
Please note these Proceedings have received limited or no review from supervisors and IIASA program directors, and the views and results expressed therein do not necessarily represent IIASA, its National Member Organizations, or other organizations supporting the work.
Last edited: 19 August 2015
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