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We study the relationship between invariant transformations on extensive gamestructures and backward dominance procedure (BD), a generalization of theclassical backward induction introduced in Perea (2014). We show thatbehavioral equivalence with unambiguous orderings of information sets, acritical property that guarantees BD's applicability, can be characterized bythe classical Coalescing and a modified Interchange/Simultanizing in Battigalliet al. (2020). We also give conditions on transformations that improve BD'sefficiency. In addition, we discuss the relationship between transformationsand Bonanno (2014)'s generalized backward induction.

Compactification of Extensive Game Structures and Backward Dominance Procedure