We consider a model of learning and evolution in games whose action sets are endowed with a partition-based similarity structure intended to capture exogenous similarities between strategies. In this model, revising agents have a higher probability of comparing their current strategy with other strategies that they deem similar, and they switch to the observed strategy with probability proportional to its payoff excess. Because of this implicit bias toward similar strategies, the resulting dynamics - which we call the nested replicator dynamics - do not satisfy any of the standard monotonicity postulates for imitative game dynamics; nonetheless, we show that they retain the main long-run rationality properties of the replicator dynamics, albeit at quantitatively different rates. We also show that the induced dynamics can be viewed as a stimulus-response model in the spirit of Erev & Roth (1998), with choice probabilities given by the nested logit choice rule of Ben-Akiva (1973) and McFadden (1978). This result generalizes an existing relation between the replicator dynamics and the exponential weights algorithm in online learning, and provides an additional layer of interpretation to our analysis and results.

翻译：我们研究了一种博弈中的学习与演化模型，其行动集被赋予了一种基于划分的相似性结构，旨在捕捉策略之间的外生相似性。在该模型中，进行策略修正的智能体更倾向于将当前策略与他们认为相似的其他策略进行比较，并以正比于观测策略收益优势的概率切换至该策略。由于这种对相似策略的隐含偏好，所产生的动力学——我们称之为嵌套复制者动力学——并不满足任何关于模仿博弈动力学的标准单调性公理；尽管如此，我们证明其保留了复制者动力学的主要长期理性性质，尽管在定量速率上存在差异。我们还证明，所导出的动力学可视为Erev & Roth（1998）提出的刺激-响应模型的一种形式，其选择概率由Ben-Akiva（1973）和McFadden（1978）提出的嵌套Logit选择规则给出。这一结果推广了现有研究中复制者动力学与在线学习中指数权重算法之间的关系，为我们的分析和结论提供了额外的解释维度。