 Iterated upgrade with \(\rat ^*\) always stabilizes to a fixed plausibility order, which is the same for all players. Identifying each history of a game with its end node allows for a belief analysis of Backward Induction (van Benthem &amp; Gheerbrant 2010). On finite trees, the histories emerging when all players resort to their Backward Induction strategies exactly correspond to the most plausible end nodes created by iterated radical upgrade with rationality-in-belief. An alternative dynamic-epistemic characterization of Backward Induction, using similar ideas in a different mix, can be found in Baltag, Smets, and Zvesper (2009).