Cooperative Behavior in a Model of Evolutionary Snowdrift Games with $N$-person Interactions

Details Cooperative Behavior in a Model of Evolutionary Snowdrift Games with $N$-person Interactions Cooperative Behavior in a Model of Evolutionary Snowdrift Games with $N$-person Interactions

2008-07-26

arxiv.org/abs/0807.4227v1

Europhysics Letters 80, 18002 (2007)

Physics

Biological Physics

4 pages, 2 figures

Scientific paper

10.1209/0295-5075/80/18002

We propose a model of evolutionary snowdrift game with $N$-person interactions and study the effects of multi-person interactions on the emergence of cooperation. An exact $N$-th-order equation for the equilibrium density of cooperators $x^*$ is derived for a well-mixed population using the approach of replicator dynamics. The results show that the extent of cooperation drops with increasing cost-to-benefit ratio and the number $N$ of interaction persons in a group, with $x^{*}\sim1/N$ for large $N$. An algorithm for numerical simulations is constructed for the model. The simulation results are in good agreements with theoretical results of the replicator dynamics.

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