The problem, as stated, seems to me like it can be solved by precommitting not to negotiate with terrorists--this seems like a textbook case.

That can work when the mugger is a terrorist. Unfortunately most muggers aren't. They're businessmen. Since the 'threat' issue isn't intended to be the salient feature of the question we can perhaps specify that the mugger would be paid $3 to run the simulation and is just talking to you in a hope of getting a better offer. You do negotiate under those circumstances.

For my part I don't like the specification of the problem as found on the wiki at all:

Now suppose someone comes to me and says, "Give me five dollars, or I'll use my magic powers from outside the Matrix to run a Turing machine that simulates and kills 3^^^^3 people."

Quite aside from the 'threat' issue I just don't care what some schmuck simulates on a Turing machine outside the matrix. That is a distraction.