In a zero-sum extensive form game, if Player A has a strategy that guarantees them a win regardless of Player B's actions, what can be inferred about the strategies employed by both players?

If Player A can win no matter what Player B does, then Player A’s plan is a dominant strategy that works in every possible game path. Because the game is zero‑sum, Player B cannot change the outcome; any strategy Player B chooses still leads to Player A’s victory. Thus Player B’s best response is irrelevant—B has no way to improve the result, so B’s strategy is essentially dominated. For example, in a simple two‑move game where A can choose a winning move first, B’s choice of a second move cannot alter the fact that A wins.