We consider a model of cultural evolution for a strategy selection in a population of individuals who interact in a game theoretic framework. The evolution combines individual learning of the environment (population strategy profile), reproduction, proportional to the success of the acquired knowledge, and social transmission of the knowledge to the next generation. A mean-field type equation is derived that describes the dynamics of the distribution of cultural traits, in terms of the rate of learning, the reproduction rate and population size. We establish global well-posedness of the initial-boundary value problem for this equation and give several examples that illustrate the process of the cultural evolution.

中文翻译：

---

战略冲突背景下的文化进化模型

我们考虑一种文化演化模型，用于在博弈论框架中进行交互的个人群体中进行策略选择。进化过程结合了个人对环境的学习（种群策略概况），繁殖，与获得的知识的成功成正比，以及知识向下一代的社会传播。推导了一个平均场类型方程，该方程根据学习率，繁殖率和人口规模来描述文化特征分布的动态。我们为此方程式建立了初边值问题的全局适定性，并给出了一些说明文化演变过程的例子。