We study the behavioral implications of Rationality and Common Strong Belief in Rationality (RCSBR) with contextual assumptions allowing players to entertain misaligned beliefs, i.e., players can hold beliefs concerning their opponents' beliefs where there is no opponent holding those very beliefs. Taking the analysts' perspective, we distinguish the infinite hierarchies of beliefs actually held by players ("real types") from those that are a byproduct of players' hierarchies ("imaginary types") by introducing the notion of separating type structure. We characterize the behavioral implications of RCSBR for the real types across all separating type structures via a family of subsets of Full Strong Best-Reply Sets of Battigalli & Friedenberg (2012). By allowing misalignment, in dynamic games we can obtain behavioral predictions inconsistent with RCSBR (in the standard framework), contrary to the case of belief-based analyses for static games--a difference due to the dichotomy "non-monotonic vs. monotonic" reasoning.

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In the leading model of bounded rationality in games, each player best-responds to their belief that other players reason to some finite level. We propose a novel behavior that reveals the player’s belief that while other players are rational, their behavior may be outside the iterative reasoning model. This encompasses a situation where a player believes that their opponent can reason to a higher level than they do. We propose an identification strategy for such behavior, and evaluate it experimentally.

This paper incorporates structural rationality (Siniscalchi, 2022) in the equilibrium and non-equilibrium analysis of dynamic games. It provides a definition of "structural equilibrium" modeled after sequential equilibrium (Kreps-Wilson, 1982) and relates it to trembling-hand perfection and quasi-perfection. It also defines "strong structural rationalizability," adapting Pearce (1984). Finally, it leverages the behavioral foundations of structural rationality to relate strong belief (Battigalli and Siniscalchi, 2002) and admissibility (Brandenburger, Friedenberg and Keisler, 2008).