I think it basically comes to, if the rational agent recognizes that the rational thing to do is to NOT buckle under blackmail, regardless of what the rational agent simulating them threatens, then the blackmailer's simulation of the blackmailee will also not respond to that pressure, and so it's pointless to go to the effort of pressuring them in the first place. However, if the blackmailer is irrational, their simulation of the blackmailee will be irrational, and thus they will carry through with the threat. This means that the blackmailee's simulation of the blackmailer as rational is itself inaccurate, as the simulation does not correspond to reality. If the blackmailee is irrational, their simulation of the blackmailer will be irrational, and thus they will concede to their demands. Yet, each party acts as if their simulation of the other was correct, until actual, photon-transmitted information about the world can impress itself into their cognitive function. So, no-one gets what they want. The best choice for a rational agent here is just to ignore the good professor. On the other hand, you can't argue with results. And there's a simulation of Quirrel s-quirreled away in your brain, whispering.

I recall the same study - and I seem to remember that the patients who knew they were being prayed for did a bit worse.