Beliefs, plans, and perceived intentions in dynamic games

We adopt the epistemic framework of Battigalli and Siniscalchi (1999) to model the distinction between a player's behavior at each node, which is part of the external state, and his plan, which is described by his beliefs about his own behavior. This allows us to distinguish between intentional and unintentional behavior, and to explicitly model how players revise their beliefs about the intentions of others upon observing their actions. Rational players plan optimally and their behavior is consistent with their plans. We illustrate our approach with detailed examples and some results. We prove that optimal planning, belief in continuation consistency and common full belief in both imply the backward induction strategies and beliefs in games with perfect information and no relevant ties. More generally, we present within our framework relevant epistemic assumptions about backward and forward-induction reasoning, and relate them to similar ones studied in the previous literature.