In recent years, a relatively abstract and general formulation of extensive form games has been developed by Carlos Alos-Ferrer and Klaus Ritzberger. The formulation is general enough to discuss when some useful properties hold- and when they fail. In particular, in [Trees and Extensive Forms][1] (WP version can be found here [here][2]), they give necessary and sufficient conditions for when every pure strategy in an extensive game induces an outcome and when this outcome is unique.  


  [1]: http://www.sciencedirect.com/science/article/pii/S0022053108000288
  [2]: http://www.univie.ac.at/vwl/Research/FWF/vie0506.pdf