We introduce the idea that a player believes at every stage of a dynamic game that his opponents will choose rationally in the future and have chosen rationally in a restricted way in the past. This is summarized by the concept of common belief in future and restricted past rationality, which is defined epistemically. Moreover, it is shown that every properly rationalizable strategy of the normal form of a dynamic game can be chosen in the dynamic game under common belief in future and restricted past rationality. We also present an algorithm that uses strict dominance, and show that it selects exactly those strategies that can be chosen under common belief in future and restricted past rationality.

中文翻译：

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对未来的共同信念和限制过去的理性

我们引入了这样一种思想，即在动态博弈的每个阶段，玩家都相信他的对手将来会理性选择，并且过去以受限方式理性选择。这是由对未来的共同信念和限制的过去理性的概念概括的，这是认识论定义的。此外，它表明，在对未来的共同信念和限制过去的理性下，可以在动态博弈中选择动态博弈范式的每一个适当合理化的策略。我们还提出了一种使用严格支配的算法，并表明它准确地选择了那些可以在对未来的共同信念和有限的过去理性下选择的策略。