Is there a game that cannot be represented by a game tree? Is there a finite game that cannot be represented by an extensive form or a game tree?

I know that many games are too long and complex to be represented by a tree of a reasonable size, but that's not what I'm looking for because it is in part a computational limitation.

Instead I wonder if there is something simple out there that just doesn't fit into an extensive form? All the books that I've read say something like 


  Various games can be represented by trees


But I haven't seen "all games" claim anywhere. Are there any known exceptions?
Well, for this you need to define what a "finite game" is. The usual way to do so, is to define it as an extensive form game, which makes the whole issue circular. But there are different ways to model extensive form games at different levels of generality. For example, the first definition due to John von Neumann and Oskar Morgenstern made a number of strong restrictions on timing that look somewhat archaic from today's perspective. The subsequent definition by Harold Kuhn significantly generalized the class of possible extensive form games. An implicit restriction in the way Kuhn defined extensive form games was that no player is allowed to move through the same information set twice, an assumption weakened in the Ph.D. thesis of John Isbell. So there are various notions of extensive form games at various levels of generality, including versions that allow for infinite games.