Cooperative Behavior in a Model of Evolutionary Snowdrift Games with   $N$-person Interactions
  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. 
D.F. Zheng, H.P. Yin, C.H. Chan, and P.M. Hui