Effects of dynamical grouping on cooperation in N-person evolutionary snowdrift game

A population typically consists of agents that continually distribute themselves into different groups at different times. This dynamic grouping has recently been shown to be essential in explaining many features observed in human activities including social, economic, and military activities. We study the effects of dynamic grouping on the level of cooperation in a modified evolutionary N-person snowdrift game. Due to the formation of dynamical groups, the competition takes place in groups of different sizes at different times and players of different strategies are mixed by the grouping dynamics. It is found that the level of cooperation is greatly enhanced by the dynamic grouping of agents, when compared with a static population of the same size. As a parameter beta, which characterizes the relative importance of the reward and cost, increases, the fraction of cooperative players f(C) increases and it is possible to achieve a fully cooperative state. Analytically, we present a dynamical equation that incorporates the effects of the competing game and group size distribution. The distribution of cooperators in different groups is assumed to be a binomial distribution, which is confirmed by simulations. Results from the analytic equation are in good agreement with numerical results from simulations. We also present detailed simulation results of f(C) over the parameter space spanned by the probabilities of group coalescence nu(m) and group fragmentation nu(p) in the grouping dynamics. A high nu(m) and low nu(p) promotes cooperation, and a favorable reward characterized by a high beta would lead to a fully cooperative state.