TITLE: Infinite games: are they well defined?
QUESTION [8 upvotes]: It is just my curiosity about this question where we have an infinite game and (according to the answers) winning strategies for both players. I am familiar with terminating games only, and I am pretty sure that nonterminating ones can cause many paradoxes. As this is a community wiki mode, I would be happy to see formal definitions, existence of wining strategies as well as possible collisions.
Thanks in advance for keeping my mind finite!

REPLY [2 votes]: 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.