"Right.  Well, I think I remember, though it's been a while, that Keltham was surprised about our oaths working because people who break them lose their Law and go to Abaddon."  Asmodia makes a mental note (an orange one, but in big letters) that this implies that Lawful Good and Lawful Neutral people wouldn't be trustworthy on quite the same level, which she should've realized earlier.  "But there's a word for something similar, in his language, something equally powerful that works without Abaddon existing there."

"So we obviously shouldn't try to figure out what that is, and actually do it, because that would maybe be more dangerous than a Golarion oath."

"But Keltham wouldn't assign us to figure that out and do it, either."

"No shit."  Who are the remaining - Ione and Tonia.  Okay, neither of those seem terribly at risk at figuring out how to make, and then break, an Algorithmic commitment.

Not that it should be even remotely possible in terms of the amount of math you'd have to invent.  But.  Thank you, Asmodia, for reminding Keltham of what kids grow up knowing before they learn too much logical decision theory.

"I'm not sure how it can be more dangerous than getting your soul devoured," Gregoria says skeptically, "but I agree that's not the answer. ...it seems possible that actually everyone defects repeatedly and then we're more motivated, when we get back, to try to figure out something better."

"That's basically what we're going to have to do if we follow the instructions to earn as much copper as we can individually, and it's annoying, and I keep trying to figure out if there's a way to - how did Keltham put it -"

"To do Something Else Which Is Not That."

"Yeah."

"Well, instead of that you could Cooperate."

"I believe this illustrates an important general principle, with which I expect the teachings of dath ilan to agree, that when you embark upon the sacred quest of doing Something Else Which Is Not That, you do not confuse this with the far less useful quest of doing Any Random Thing Whatsoever That Is Not That or, worse yet, doing An Even Stupider Thing Which Is Not That."

"Well, I picked you as my partner because I figured if anyone was going to think of Something Else Which Is Not That it'd be you, so, go on, think of it."

Asmodia wonders if this is how her hypothetical goddess feels all the time.

Tonia and Ione.

 "- one of us needs to be the sort of person who'll Cooperate if the other person Cooperates, and the other person needs to be the sort of person who's going to Cooperate given that, and we both try to read each other past what might be a bluff about that being true.  We're not breaking Keltham's rules, that just is how you earn the most copper."

"Well, are you the sort of person who's going to Cooperate?"

"I sure would if I thought you were the sort of person who'd Cooperate if you thought I would Cooperate!  Though I'd probably also want to ask you things like, is your Sense Motive good enough that you can read me?"

"And if I can't read you, and you know that, then you'll defect. All right," says Tonia. In a way it's a very Asmodean game. "Well, if that's what we're supposed to do to get the most copper, I'll try it. I'll Cooperate if I think you'll Cooperate." Which she doesn't think at all.

"Bluff.  Now you know my Sense Motive isn't that terrible."

"I'll Cooperate if I think you'll Cooperate."  (Truth.)

Tonia bites her lip. "But you don't think I'll Cooperate, so you don't in fact plan on Cooperating."

"But I am sincere about Cooperating if you Cooperate, which reduces this to the problem of, first of all, you actually intending to Cooperate, and second, once that happens, my being able to read you about that."

"I'll cooperate, if you'll cooperate," says Tonia. (She's confused enough she's not sure if this is true. Probably not.)

"Now you're feeling confused but trying to go along with things, and the reason I know this, is, that's not what you'd say if you were tracking this."

"If I'm like 'I'll cooperate if I think you'll cooperate' and you're like 'I'll cooperate if I think you'll cooperate' then where does that leave us, nowhere, is where it leaves us, unless and until somebody can be like, okay, I'll cooperate.  Now I already told the truth about cooperating if I think you'll cooperate, and I think you know that, so what you need to do now, is just decide to cooperate."

Maybe Ione can get Asmodia to overrule Tonia about what alter-Asmodeans would do here...

...actually, if the wizard students weren't already familiar with first-order logic, the chances are roughly infinity to zero against them already being familiar with the principle that (for most proof systems put together the obvious way) you may freely assume a proposition's quoted provability within a quoted system, in order to prove the unquoted proposition within the unquoted system.

Without which principle the problem of 'I have to know/prove/guess-with-sufficient-probability your decision before I can decide' is in fact unsolvable.  Oops.

Well, you could state about yourself that you were adopting some informal version of that principle, it's not like humans actually meet the assumptions for the simple version of the math.  But, yeah, that probably makes it a lot harder to see how the solution works, doesn't it.

"But it'd be stupid for me to just decide to cooperate without any caveats!" objects Tonia.

"You're not!  You're deciding that after you read my sincerity about Cooperating if you Cooperated!  Otherwise it'd be stupid, yeah, which is why I didn't just say, I've decided to Cooperate."

" - okay. So, I'm saying, since I can't bluff you, and since if you actually read me as planning on Cooperating you'll Cooperate, that means I'm just better off, if I cooperate, since you can tell. Unless you've changed your mind since when you said that thing, say it again."

"I will definitely Cooperate if I think you'll definitely - no, if I think it's pretty likely, reasonably likely, that you'll Cooperate."

"You're currently confused, suspicious, sort of testing the waters there, but not in an insincere way.  You're sort of trying to make up your mind about it and see what happens, but you haven't really made up your mind.  This is progress!  And I don't want to just say, you don't get rewarded at all, for coming a little further.  So, even if you don't get any further than that, if you stay in just this state of mind, I'll spin a coin three times, and if it comes up Queen each time, I'll Cooperate with you.  That's about how likely I think you are to really Cooperate in what appears to be your current state of mind.  We've made progress, now try taking it a step further."