What is the game tree algorithm?

Is to use the nodes of the tree to represent each step in the game process. For example, in chess, both sides get the same board information. They take turns playing chess in order to kill each other or avoid being killed.

So we can use a "game tree" (an N-tree) to represent the process of playing chess-each node in the tree represents a situation on the chessboard, and different situations (new nodes) are generated for each situation (node) according to different moves, and so on until there is no alternative move, that is, reaching the leaf node (the game is over).