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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 (WP version can be found here here), they give necessary and sufficient conditions for when every pure strategy in an extensive game induces an outcome and when this outcome is unique.