 In the top node of the leftmost tree, going right is not dominated in beliefs for player A by going left. So, \(\rat ^*\) only affects E’s turn, and radical upgrade with \(\Uparrow\rat ^*\) makes \((0, 3)\) more plausible than \((2,2)\) . After this change, going right has become dominated in beliefs in the top node, and a new upgrade takes place, making A’s going left most plausible.