We introduce consistency of beliefs in the space of hierarchies of conditional beliefs (Battigalli and Siniscalchi) and use it to provide epistemic conditions for equilibria in finite multi-stage games with observed actions.

Brandenburger et al. (2008) establish epistemic foundations for admissibility, or the avoidance of weakly dominated strategies, by using lexicographic type structures and the notion of rationality and common assumption of rationality (RCAR). Their negative result that RCAR is empty whenever the...