We analyze the sequential structure of dynamic games with perfect information. A three-stage account is proposed, that species setup, reasoning and play stages. Accordingly, we define a player as a set of agents corresponding to these three stages. The notion of agent connectedness is introduced into a type-based epistemic model. Agent connectedness measures the extent to which agents' choices are sequentially stable. Thus describing dynamic games allows to more fully understand strategic interaction over time. In particular, we provide suffcient conditions for backward induction in terms of agent connectedness. Also, our framework makes explicit that the epistemic independence assumption involved in backward induction reasoning is stronger than usually presumed, and makes accessible multiple-self interpretations for dynamic games
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