The solution is contained in the post. I can't find a problem with it. It was you who were suggesting this is a naive analysis. Equilibria just seem to me to b

The solution is contained in the post. I can't find a problem with it. It was you who were suggesting this is a naive analysis. Equilibria just seem to me to be the wrong tool for the job, you have to (as you have) invent a related infinite game with additional axioms and expectations before that kind of analysis kicks in. Check your responses. If you can't describe what you're trying to say without mentioning anyone 'changing' their strategy, or assuming that a strategy is default, then you've got the wrong framework, I'd suggest (modulo my admitted lack of specific expertise).