 In the matrix game, no move dominates any other. Hence E should consider all outcomes possible. In this case, going left is safer for her than going right, and hence A should play Left at the start. However, if E rationalizes, and observes A going Right, she has extra information available at her choice node. Following the rationality assumption, A expects to do better than 3, which is only possible if he intends to play Up in the matrix game. Now this tells E to proceed to the matrix and play the left column therein. E’s results in a better payoff than the 2 of her original safe option.