___________is a tree in which the nodes represent game states and the edges represent player movesBinary treeSearch treeGame treeRoot tree

The correct answer is Game tree.

Explanation:

A game tree is a specialized structure used in game theory and artificial intelligence to represent various game states and the possible moves within a game. Each node in a game tree denotes a specific state of the game, while the edges illustrate the possible moves a player can make to transition from one state to another.

In contrast, a binary tree is a data structure where each node has at most two children, and a search tree is typically utilized for organizing data to allow for efficient searching, insertion, and deletion. A root tree does not specifically refer to game states or player actions but rather denotes a general concept of the root node in any hierarchical data structure.

Thus, when considering trees in relation to games and player strategies, a game tree is the most applicable term. It allows for analysis of all potential outcomes based on different player decisions, making it a fundamental concept in strategies for games like chess or tic-tac-toe.