argumate

And that's gonna be the end of that topic. Well, I mean, it will be the last thing I have to say about the MIRI modal logic prisoner's dilemma tournament. I expect to have more to say with provability logic, I just only really have one thing to say about this specific game or exercise or whatever.

CooperateBot: Always cooperate

FairBot: i'll cooperate if I can prove you cooperate

PrudentBot cooperates with FairBot, but its advantage over FairBot is that it defects on CooperateBot, thus achieving a higher score

The PrudentBot definition was weird, definitely non-trivial

By the way, the original iterated prisoner's dilemma tournament has a non-trivial bot too, but developed many years later. Maybe this was because Axelrod would rather write a book on how nice guys win after all than improve on Tit-For-Tat, or maybe just because it really is non-trivial (I don't really understand the paper yet, to be honest).

but still, how many possible combinations are there in total, 16?

you cooperate with me if I cooperate with you (Y/N)

you cooperate with me if I defect against you (Y/N)

CooperateBot _ _ => Y

DefectBot _ _ => N

FairBot Y _ => Y FairBot N _ => N

PrudentBot Y N => Y PrudentBot Y Y => N PrudentBot N _ => N

UnfairBot = ~FairBot

ImprudentBot = ~PrudentBot

and a bunch of others, like uh one that only rewards naivety:

SuckerAppreciatorBot Y Y => Y SuckerAppreciatorBot Y N => N SuckerAppreciatorBot N _ => N

or the inverse that rewards anything but naivety

BUT. What you're talking about here is not MIRI's tournament.

To be clear, what you're discussing is how i think the bots should work. Like, they make some kind of "report", which says this is what happens if I cooperate and this is what happens if I defect. There's four possible reports, and thus 16 possible ways to act on the reports.

But that's not how the MIRI bots work! FairBot is "if I can prove you cooperate, I'll cooperate; otherwise, I'll defect". Otherwise, as in, if there's no such proof.

All of MIRI's proof-based decision stuff was in terms of these kinds of fallback options in the absence of a proof. One of the authors on the prisoner's dilemma paper proposed a general decision theory of that kind a few years later.

It made the prisoner's dilemma tournament very weird. It's weird enough that they were able to run it at all with a real computer rather than an imaginary provability oracle. As I understand it that's just because for all of the bots they actually implemented, the matches were decidable in provability logic. So it worked because provability logic is decidable and arithmetically complete.

But it made the bots themselves weird, because they had to introduce bots that check what their opponent does against other bots. PrudentBot checks if its opponent defects on CooperateBot.

This created a ladder of bots: if I'm a rank-k bot, I check what you do against me, but also against rank-(k-1) bots.

One of the results in the paper is that there's no rank-0 PrudentBot: all rank-0 bots that cooperate with FairBot also cooperate with CooperateBot. So the ladder is necessary.

And that gets you an infinite zoo of bots.

I'm thinking now that this was all due to a mistake setting up the tournament.

Look, this isn't a game like on Steam; this is game theory. Personally, I don't want the game to be interesting to play. I want to be able to prove some optimal strategy. I think there should be only 16 bots.

And that's gonna be the end of that topic. Well, I mean, it will be the last thing I have to say about the MIRI modal logic prisoner's dilemma tournament. I expect to have more to say with provability logic, I just only really have one thing to say about this specific game or exercise or whatever.

CooperateBot: Always cooperate

FairBot: i'll cooperate if I can prove you cooperate

PrudentBot cooperates with FairBot, but its advantage over FairBot is that it defects on CooperateBot, thus achieving a higher score

The PrudentBot definition was weird, definitely non-trivial

By the way, the original iterated prisoner's dilemma tournament has a non-trivial bot too, but developed many years later. Maybe this was because Axelrod would rather write a book on how nice guys win after all than improve on Tit-For-Tat, or maybe just because it really is non-trivial (I don't really understand the paper yet, to be honest).

but still, how many possible combinations are there in total, 16?

you cooperate with me if I cooperate with you (Y/N)

you cooperate with me if I defect against you (Y/N)

CooperateBot _ _ => Y

DefectBot _ _ => N

FairBot Y _ => Y FairBot N _ => N

PrudentBot Y N => Y PrudentBot Y Y => N PrudentBot N _ => N

UnfairBot = ~FairBot

ImprudentBot = ~PrudentBot

and a bunch of others, like uh one that only rewards naivety:

SuckerAppreciatorBot Y Y => Y SuckerAppreciatorBot Y N => N SuckerAppreciatorBot N _ => N

or the inverse that rewards anything but naivety

I ran across this lecture/talk awhile back and, in summary, the guy works to build a historically accurate ark based on descriptions from the Epic of Gilgamesh. And they used bitumen ie tar to coat the boat in the epic and then in modern day.

And that's gonna be the end of that topic. Well, I mean, it will be the last thing I have to say about the MIRI modal logic prisoner's dilemma tournament. I expect to have more to say with provability logic, I just only really have one thing to say about this specific game or exercise or whatever.