Given a marked game tree, the unique path that leads from the root \(v_0\) of the game tree to the outcome with the utilities that match the utilities assigned to \(v_0\) is called the backward induction path. In fact, the markings on each and every node (even nodes not on the backward induction path) defines a unique path through the game tree. These paths can be used to define strategies for each player: At each decision node \(v\), choose the action that is consistent with the path from \(v\). Let \(BI\) denote the resulting backward induction profile (where each player is following the strategy given by the backward induction algorithm).