# Game tree vs. extensive form of a game

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?

• The wikipedia page you linked (en.wikipedia.org/wiki/Extensive-form_game) indicates that some authors view the extensive form as being the same as the game tree. – quasi Mar 3 '18 at 2:47
• @quasi Yes, I noticed that. I am wondering if this equivalence is appropriate. It does not seem like they are equivalent representations to me. – jonem Mar 3 '18 at 3:00
• When you say that the nodes in the extensive form "don't represent states", do you have a reference for that? – quasi Mar 3 '18 at 3:05
• @quasi In games with actions that have probabilistic effects, the action itself cannot characterize the state (for example, where I take action $a$ in state $s$ and I end up at state $s'$ with probability $0.5$ or state $s''$ with probability $0.5$). – jonem Mar 3 '18 at 3:08
• The state at a given node consists of all the information known to the player who is at that node, including probabilistic effects, and their associated probabilities. – quasi Mar 3 '18 at 3:29