Imagine a similar game to Chess, called Pursuit-Evasion. There are two players: the Pursuer (P) and the Evader (E). The game ends only when both P and E end up at the same node, i.e., when the Pursuers catches the Evader. Consequently, we can see that if the game terminates, then P wins; otherwise if the game does not terminate, then E wins. Consider the following simplistic game map: Can you prove who always wins this game? And in general, if the game map is a tree like above, can you say anything about who always wins such tree-games