具有$N$ -人交互的雪堆演化对策模型中的合作行为
Cooperative Behavior in a Model of Evolutionary Snowdrift Games with $N$-person Interactions
摘要：
提出了一个具有$N$ -人交互的进化雪堆博弈模型，研究了多人交互对合作出现的影响。本文利用复制子动力学方法，导出了一个精确的$N$ -阶方程，该方程描述了一个完全混合的种群中合作者$x^*$的平衡密度。研究结果表明，合作程度随着成本收益比和群体中交互人数的增加而下降，其中$x^{*}\sim1/N$为大$N$。为该模型构造了一个数值模拟算法。模拟结果与复制子动力学的理论结果吻合较好。
英文摘要：
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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