You don't get tired at all... there is no cost at all...

So you have deliberately constructed a scenario, then defined "winning" as something forbidden by the scenario. Unhelpful.

That's multiple solutions.

You have specified multiple games. I have defined a finite set of solutions for each Actor that can all be stated as "use the stopping function". If your Actor has no such function, it is not rational because it can get stuck by problems with the potential to become unbounded. Remember, the Traveling Salesman must eventually sell something or all that route planning is meaningless. This sort of thing is exactly what a stopping function is for, but you seem to have written them out of the hypothetical universe for some (as yet unspecified) reason.

A reader can't go to the author and demand volume 2...

Incorrect. People do it all the time, and it is now easier than ever. Moreover, I object to the comparison of your essay with a book. This context is more like a conversation than a publication. Please get to the point.

My objective is to convince people of this abstract theoretical point...

You have done nothing but remove criteria for stopping functions from unbounded scenarios. I don't believe that is convincing anybody of anything. I suspect the statement "not every conceivable game in every conceivable universe allows for a stopping function that does not permit somebody else to do better" would be given a non-negligible probability by most of us already. That statement seems to be what you have been arguing, and seems to coincide with your title.

Friendly Style Note: I (just now) noticed that you have made some major changes to the article. It might be helpful to isolate those changes structurally to make them more visually obvious. Remember, we may not be rereading the full text very often, so a timestamp might be nice too. :)