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In dynamic settings each economic agent's choices can be revealing of herprivate information. This elicitation via the rationalization of observablebehavior depends each agent's perception of which payoff-relevant contingenciesother agents persistently deem as impossible. We formalize the potentialheterogeneity of these perceptions as disagreements at higher-orders about theset of payoff states of a dynamic game. We find that apparently negligibledisagreements greatly affect how agents interpret information and assess theoptimality of subsequent behavior: When knowledge of the state space is only'almost common', strategic uncertainty may be greater when choices arerationalized than when they are not--forward and backward inductionpredictions, respectively, and while backward induction predictions are robustto small disagreements about the state space, forward induction predictions arenot. We also prove that forward induction predictions always admit uniqueselections a la Weinstein and Yildiz (2007) (also for spaces not satisfyingrichness) and backward induction predictions do not.

Heterogeneously Perceived Incentives in Dynamic Environments: Rationalization, Robustness and Unique Selections