I am a bit confused by the following statement from the Game Tree wikipedia page:
the complete tree is the same tree as that obtained from the extensive-form game representation
A game tree consists of nodes that represent different states of the game and how different actions can lead to different states. As far as I understand, the extensive form representation of a game consists of nodes that do not represent states, rather they indicate which player should make the decision at that node.
Furthermore, it is known that there may be more than one extensive form game representing the same strategic interaction. I don't believe the same is true for a game tree.
Can anyone clear up my confusion?