中文摘要：

首先定义了具有确定分布的随机环境中的基于适应度的平均选择算子，然后证明了主体战略集上的任一概率密度在平均选择算子的迭代过程中收敛于平均适应度函数的最大集上的某一分布，然后就多主体的博弈问题定义了平均选择算子，并以此为基础证明了平均选择算子的不动点就是博弈的纳什均衡。

英文摘要：

Average selection operators in random environments are introduced in the first place, and it is proved that the sequence of probability distributions in agents＇ strategies set, when repeatedly operated by average selection operator, converges to the probability distribution in the subset of strategies that takes the largest value of average fitness. Then, the concept of average selection operator is extended to the multi-agents game problems, and it is proved that the fixed points of such an operator are just the Nash equilibria of games.