Abstract This paper introduces a novel replicator equations to cover evolutionary games. This replicator is applied on a finite set of agent communities organized on arbitrary graphs. The communities located at the nodes of the graph compete with their neighbours according to the weights of the links that connect them. The communities replicate by imitation probabilities those neighbourhood’s strategies with higher utility. The communities also execute a best response addressed to maximize the entropy associated to imitation probabilities. We explore possible connexions between our replicator equations and The Second Law of Thermodynamics, and prove that populations reach consensus equilibria as expressions of maximum entropy states. We also explore connexions with learning dynamics, and prove that under suitable assumptions and conditions, the communities carry out and intelligent learning process. We illustrate results with an example of the classical hawk-dove game applied on fully-connected and arbitrary populations.

中文翻译：

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有限和任意网络社区的基于模仿的复制器

摘要 本文介绍了一种新的复制方程来涵盖进化博弈。该复制器应用于在任意图上组织的一组有限的代理社区。位于图中节点的社区根据连接它们的链接的权重与其邻居竞争。社区通过模仿概率复制那些具有更高效用的社区策略。社区还执行最佳响应以最大化与模仿概率相关的熵。我们探索了我们的复制方程和热力学第二定律之间可能的联系，并证明种群达到共识平衡作为最大熵状态的表达。我们还探索与学习动态的联系，并证明在合适的假设和条件下，社区开展智能学习过程。我们通过一个应用于全连接和任意种群的经典鹰鸽游戏的例子来说明结果。