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Following your interesting theory, I have some concerns: 

1. In carrying out that recursion, if "freeing the roles" means killing the actor/actress of those roles, won't that kill the mc too, since he plays Zeus in that play?(technically everyone else who's playing any role would die but Asterion technically is unkillable as long as he's still under the labyrinth's magics, if that works out then he'd be truly freed)

2. We're still missing an important role, Hera's - the rightful wife of Zeus who got jealous of her husband's affairs and started the whole imprisonment in the first place.

And please talk more about the ancient Greek mythology since I'm complete ignorant on this but would still love to enjoy the theory crafting of this game no matter how busy I am with the real world OTL

Not necessarily: he has to to kill the person playing "Argos" because, in the story, "Hermes" kills "Argos." Which is what sets "Io" free. So, presumably, his reasoning is that Asterion is in captivity, making him count as "Io" and then freeing "Io" will undo that. If that is his plan, and if it works, then presumably nobody else has to die.

So I guess in this case, the role of "Hera" would be Athena? As the architect of "Io"'s captivity whom Hermes is thwarting.