I am denying that superintelligences play this game in a way that looks like “Pick an ordinal to be your level of sophistication, and whoever picks the higher ordinal gets $9.” I expect sufficiently smart agents to play this game in a way that doesn’t incentivize attempts by the opponent to be more sophisticated than you, nor will you find yourself incentivized to try to exploit an opponent by being more sophisticated than them, provided that both parties have the minimum level of sophistication to be that smart.
If faced with an opponent stupid enough to play the ordinal game, of course, you just refuse all offers less than $9, and they find that there’s no ordinal level of sophistication they can pick which makes you behave otherwise. Sucks to be them!
Wow, that’s fucked up.