 The classical argument for backwards induction implicitly assumes that at each stage of the game, the agents discount the preceding moves as strategically irrelevant. Defenders of the classical argument can argue that this assumption makes sense, since by definition at any agents’ decision node, the previous moves that led to this node are now fixed. Critics of the classical argument question this assumption, contending that when reasoning about how to move at any of his information sets, including those not on the backwards induction equilibrium path, part of what an agent must consider is what conditions might have led to his being at that information set. In other words, agents should incorporate reasoning about the reasoning of the previous movers, or forward induction reasoning, into their deliberations over how to move at a given information set. Binmore (1987) and Bicchieri (1993) contend that a backwards induction solution to a game should be consistent with the solution a corresponding forward induction argument recommends. As we have seen, given common knowledge of the game and of rationality, forward induction reasoning can lead the agents to an apparent contradiction: The classical argument for backwards induction is predicated on what agents predict they would do at nodes in the tree that are never reached. They make these predictions based upon their common knowledge of the game and of rationality. But forward induction reasoning seems to imply that if any off-equilibrium node had been reached, common knowledge of rationality and the game must have failed, so how could the agents have predicted what would happen at these nodes?