I think the intuition that such infinite games make sense requires the axiom of determinacy to be well founded. The axiom of determinacy has been known to contr

I think the intuition that such infinite games make sense requires the axiom of determinacy to be well founded. The axiom of determinacy has been known to contradict the axiom of choice since the early 1960s (i.e. it is inconsistent to have both the axiom of choice and the axiom of determinacy).