Before revision:  The compact extensive form provides an approach to avoid problems in dynamic game theory due to the vague definition of the chronological order of the moves, for example, belief in the opponents' future rationality ( Perea ( 2014))'s sensitivity to the specific extensive form representation. We show that any strategy which can rationally be chosen under common belief in future rationality in a minimal compact game if and only if it satisfies this property in every extensive form game which is related to it via some compactification process .
After revision:  The compact extensive form provides an approach to avoid problems in dynamic game theory due to the vague definition of the chronological order of the moves, for example, belief in the opponents' future rationality ( Perea ( 2014). We show that behavioral equivalence with unambiguous orderings of information sets, a critical property that guarantees BD's applicability, can be characterized by the classical Coalescing and a modified Interchange/Simultanizing in Battigalli et al. (2020). We also give conditions on transformations that improve BD's efficiency. In addition, we discuss the relationship between transformations and Bonanno (2014)'s generalized backward induction .