I agree with what Dave says in his comment, which is basically that you could have a very generic pre-commitment strategy.

But suppose you couldn't come up with a very generic pre-commitment strategy or that it is really implausible that you could come up with a pre-commitment solution at all before hearing the rules of the game. Would that mean that there are no pre-commitment solutions? No. You've already identified a pre-commitment solution. We only seem to disagree about how important it is that the reasoner be able to discover a pre-commitment solution quickly enough to implement it.

What I am saying is that the logic of the problem does not depend on the reasoning capacity of the agent involved. Good reasoning is good reasoning whether the agent can carry it out or not.

Also, sorry if I jumped too hard.