Ben: Hey, Liz.

Liz: Hey Ben.

Ben: Should we just enter introduce ourselves now? Hi, I'm Ben Klemens.

Liz: I'm Liz Landau

Ben: And this is

Both: Pod Paper Scissors.

[Opening theme. "You've gotta make decisions."]

Liz: You know Ben I've been thinking, we haven't gone back to the Prisoner's Dilemma in a while.

Ben: Yeah, that was Episode Two. It's always got to be really early in any sort of game theory—We're the _only_ game theory podcast. So I guess I'm right in saying it's got to be really early in any game theory podcast.

Liz: But some of you who have joined us more recently, and for those of you who have been with us the whole time, we want to give you more of the Prisoner's Dilemma.

Ben: There's so much more.

Liz: In fact, it doesn't even have to be about prisoners.

Ben: Yeah, in fact, I always kind of disliked the story of prisoners in interrogation rooms. It's kind of like, the Prisoner's Dilemma has so many applications, we don't need a contrived example.

Liz: Yeah, like for example, let's say I have a roommate, and her name is Chellie. Chellie, and I share a kitchen. And sometimes we notice that a lot of dishes pile up in the sink because somebody has to take responsibility for loading and unloading the dishwasher.

Ben: Ideally, you just hang out and let Chellie do the dishes, and Chellie, she's probably just hanging out, hoping that you will do the dishes.

Liz: Right? And so if neither of us actually move dishes into the dishwasher, then we're just gonna have a really cluttered kitchen of dirty dishes.

Ben: Yeah, and if you work together, then you both put out some effort.

Liz: Yeah, but if one of us is always doing the work, and the other one is just chillin, then the one who's just doing all of the work is going to feel resentful of the chillin' one.

Ben: Chillin' Chellie.

Liz: Chillin' Chellie.


Ben: Game theoretically, the core point of it is that ideally, everyone coöperates and the dishes get done quickly. But everyone always has the incentive to slack off and let other people do the work, or just be uncooperative, as per our theme song. Did we only play the theme song in full in the first episode?

Liz: That's true. However, we can end on that note.

Ben: Yeah, let's do that. On those notes. That said anyway, yeah, so your options are to coöperate or defect. And so that's pessimistic. The only equilibrium in the Prisoner's Dilemma is for both people to just shirk to defect and then you wind up with a sink full of dirty dishes. This is often the storyline for environmental issues. I don't want to get a converter for my car to scrub pollutants out of my car, but I want everyone else to.

Liz: Yeah, well, actually, we're going through that right now with the COVID vaccine. There are people out there who just want everyone else to get the COVID vaccine so that they don't have to and they can just ride on the immunity of the population.

Ben: Yeah, so there are a million examples of this and it's always pessimistic. It's always just an appeal to people. Yeah, really, be nice, don't defect. But there's a way out, which is the iterated Prisoner's Dilemma.

Liz: The iterated Prisoner's Dilemma. What do you mean, iterated?

Ben: Repeated.

Liz: What do you mean? iterated?

Ben: I mean, repeated.

Liz: What do you mean iterated?

Ben: Economists have to sound pretentious, So instead of just saying repeated...

Liz: Oh

Ben: Yeah, anyway, so the iterated Prisoner's Dilemma? Well, you do it again. You and Chellie, you you both have dinner on Monday, and then you have dinner again on Tuesday. Perhaps how you did the dishes on Monday will affect what you did on Tuesday.

Liz: Oh, yeah. Like if one of us harbors resentment towards the other and it just builds up like a pile of dirty dishes. That's not going to be a very harmonious situation. Now is it?


Ben: Back to theory land, Robert Axelrod, in the 80s, he ran a tournament. He ran a computer tournament.

Liz: Oh, I think I heard a Radiolab episode about this.

Ben: Oh, you probably have. It's a story that's been told many times before.

Liz: It is about tit for tat.

Ben: Yeah, that's where we're gonna wind up.

Liz: Yeah. So remind me what—Robert Axelrod has some kind of competition for the best solution to the Prisoner's Dilemma?

Ben: Yeah, he sent out a call to a bunch of his game theorist friends. Oh, but by the way, we'll get to this in a second, but yeah, he sent a sample program and told them like this is the input and output. You're gonna send me a FORTRAN or a BASIC program in return that plays the Prisoner's Dilemma repeatedly.

Liz: This must have been a very long time ago.

Ben: Yes. People mailed computer code. [Liz: Whoa] And then Axelrod et al., they they got together and they ran this tournament. So they programmed it up and set the thing up to... I think, like 12,000 times or so each little robot that got sent in would play against the other robots, and then they would keep the total score. And so in the Radiolab episode, in—Yeah, I mean, I looked at the transcript before. Should we act surprised? Like, I didn't look at the transcript. Like, [exaggerated voice of wonder] Whoa, what happened in the Radiolab episode, Liz. I didn't look at the transcript beforehand.

Liz: So we've learned that tit for tat was the ideal strategy.

Ben: [voice of wonder] What's that Liz?

Liz: Tit for tat is when one person does something and the other person mirrors that behavior. For example, if I were to unload the dishwasher—

Ben: On day one, on Monday

Liz: —and my roommate Chellie does not put the next batch of dishes into the dishwasher—

Ben: on Monday

Liz: —then I will be less inclined to unload the dishwasher—


Ben: On Tuesday. So what happens on Tuesday,

Liz: Either the dishes pile up or Chellie has to do it.

Ben: Okay, so let's say Chellie does it on Tuesday, then what happens on Wednesday,

Liz: Then I'm more inclined to pitch in to do the dishes the next time.

Ben: Okay, so you're just gonna do whatever Chellie did yesterday.

Liz: Yeah, that's it.

Ben: That sounds extremely reasonable. And in fact, you may have heard this on Radiolab, the tournament was won by tit for tat tat. People sent in lots of weird strategies that, you know, went for pages and pages of FORTRAN code. And tit for tat was the shortest strategy in the system. He said it was like five lines of code.

Liz: Wow, someone actually mailed five lines of code.

Ben: Axelrod ran the tournament, so I think he uh—anyway, it doesn't matter. And you know, the sample program that got sent out, it wasn't much longer anyway. Yeah, so that's the that's the story as usually told. And we don't have a grant from the Alfred P. Sloan Foundation,

Liz [Public radio announcr voice]: advanced understanding of science and technology in the modern world.

Ben: I'm sorry, I shouldn't make fun of Radiolab; we're both fans. And in fact, Liz knows Latif pretty well.

Liz: Latif is a good friend of mine.

Ben: So, Liz, let me tell you the secret history behind tit for tat.

Liz: Wait, what secret history?

Ben: That sample program, that was called tit for two tats.

Liz: Wait, I have two tits, But no tats. How can you have tit for two tats?

Ben: Yeah, well, we can talk about two tits for a tat later, believe it or not. But anyway, the point of tit for tat is that you you try to empty the dishwasher on Monday. And then if Chellie doesn't, on Tuesday tit for tat would say that you don't do it either. You do whatever Chellie did yesterday. But you presume, okay, maybe Chellie just screwed up. Maybe she got drunk and fell asleep or something, but meant well.


Liz: , so I mean, maybe she like went for a hike and came back really late. And just like, you know, forgot.

Ben: Yeah, stuff happens. On Tuesday, you cooperate anyway, even though Chellie defected on Monday.

Liz: Oh, I get for the benefit of the doubt.

Ben: Yes. But if she if she defects twice in a row, then screw it. She's not, she's not on the team. And so you defect once.

Liz: Oh.

Ben: And then if Chellie cooperates that on Wednesday, go ahead. The clock is reset. And you're both coöperating again. Tit for two tats. It's more forgiving, because it you know, IRL, especially, yeah, sometimes there are misunderstandings.

Liz: I like that it's a good model of forgiveness. And the benefit of the doubt.

Ben: Yeah, I mean, I feel like this comes up in fiction a lot. This sort of test of trust. [Liz hums the Game of Thrones theme.] That means Liz has Game of Thrones examples.

Liz: I just can't even narrow down a single example. I mean, throughout Game of Thrones, such as when Jamie Lannister—spoiler alert—kind of betrays the Lannisters and comes over to the cause of the Starks, like he kind of has to prove his loyalty. And people are very suspicious of him, but they kind of give him the benefit of the doubt, as in they don't behead him. So yeah also Varys the spy he seems to just like, be everywhere at all times. He must actually be traveling at the speed of light because he appears in like multiple scenes back to back in completely different locations. Very suspicious, and—

Ben: And Liz is about to relive all ten seasons.


Liz: By the way, there were only seven seasons.

Ben: You're just gonna make up extra. I just know it. It's also a favorite on sitcoms, where somebody kind of hear something or, you know, misunderstands something, then they have to decide, okay, am I going to assume the other person is defecting? Or do I forgive them and wait until the next period and see what they do? And of course, in sitcoms the person is always doing—like it's always a big misunderstanding, right? And if one side punishes defection, then there's this embarrassing scene where they find out that no, the person did not defect. They just misheard through the kitchen door, yeah.

Liz: Yeah.

Ben: Yeah.

Ben: Yeah. Axelrod wrote in his write up of the of the tournament, he ran the tournament, tit for tat won. Out of all of the strategies, it did best, it got the best scores on those 12,000 rounds against every opponent. But that was official, that was the ones who actually mailed things in. But he's sitting there in the computer lab, and he's like, well, I wrote this stupid sample program, let's run that too. And it won.

Liz: Oh, so his own program won?

Ben: Yeah, yeah, the stupid sample program won the tournament, but nobody entered it. So it, so formally speaking, yes, tit for tat won the tournament, but he threw in this extra strategy, and it did better.

Liz: Okay, so next time, Chellie forgets to give me a birthday present, even though I gave her a birthday present, I'm gonna give her the benefit of the doubt and can stay friends with her.

Ben: In fact, being nice helps. One of the big lessons from the tournament. The top eight contenders are all what Axelrod calls nice, in the sense that they don't defect first. They always coöperate until the other side does, like doesn't do the dishes. And then all of the ones below the top eight, they at some point weren't nice. Tit for two tats shows that relative to tit for tat, yeah, being nicer can help. But wait, there was a second round of the tournament.

Liz: A second round?

Ben: There was a second round, tit for two tats did not win that one.


Liz: Oh, no. So who won?

Ben: Tit for tat won. Oh, Axelrod's lesson from this. Was that in that second round, people were meaner. There were fewer nice strategies. There are different environments. In some environments, yeah. People are generally nice. And there's reason to give them benefit of the doubt. In other situations, people are kind of terrible, right? The big lesson from tit for tat versus tit for two tats—Oh, and by the way, two tits for a tat means every time Chelli doesn't do the dishes, you don't do the dishes for two days in a row.

Liz: Oh, right. And that never really does better in Axelrod's experiments. But the lesson was that doing like exactly one for one correspondence doesn't necessarily make sense in all contexts. Sometimes, yeah, you should be more suspicious. And sometimes, generally speaking, yeah, you should give more benefit of the doubt.

Liz: I can think of some other examples. Like, let's say you invited your friend Sillie to a birthday party. But then Sillie didn't invite you to her birthday party. And then the next time you have a party, you have to ask yourself, should I invite Sillie when everybody's talking about the great party that she had, that I wasn't invited to?

Ben: Yeah, that's a hard one. [Pause] That pause means I have no idea what to do in that situation.

Liz: If only we were as knowledgeable as Miss Manners.

Ben: I think Miss Manners would advise that you ignore the perceived slight.


Liz: Oh, then Miss Matters with a tit for two tats kind of person?

Ben: Absolutely. I think especially since she got so many letters from people who were like, my cousin did this thing, and it was the rudest thing on earth, blah, blah, blah. Miss Manners is like, you are reading into this. Just take a deep breath, yeah.

Liz: And, you know, I think that the repeated Prisoner's Dilemma emphasizes that in real life, we have ongoing relationships with people, not only in a romantic sense, but in a friendship sense in a work sense, in a living situation sense. You can't just defect and then walk away. Like if you're gonna have dinner with your friend at the end of your lovely meal, if you're like, well, checks on you, and you just run away, your friend isn't going to like you very much. You might have saved some money, but you've lost a friend.

Ben: Yeah, that's definitely worse than not inviting somebody to a party.

Liz: Is it?

Ben: Well, see, when I write invite list for parties, I forget, I always forget somebody.

Liz: I know I still have regrets about that.

Ben: It's one of the hardest things that I can do. Math is much easier. I would rather do a page of algebra homework than try to work out go through my address book and pick out the people who I should bring to a game day or something.

Liz: Oh, yeah. Ben's heavy game day in July if you haven't received an invite.

Ben: Yeah, it's on me, okay, great. We could talk about the Prisoner's Dilemma a lot more times. Is it okay, if we iterate and talk more about the Prisoner's Dilemma next time?

Liz:That sounds great, Ben.

Ben: Yeah, because we've got caterpillars. We've got caterpillars and contractors. I think that's going to be the title of the next episode.

Liz: Caterpillars and contractors.

Ben: Yeah, yeah. So we'll find out about that next time on

Both: Pod, Paper Scissors.


Liz: Oh, it's been a while since we've heard the theme song...

Ben: Oh, yeah. Hit it Liz.

Liz: Who says that everything we do makes sense?
We're all just playing games of self-defense.
Is it Chicken, is it Chess?
Is the problem zero sum,
or a Prisoner's Dilemma, that will reach an equilibrium?

You gotta make decisions.
Will you coöperate or defect?
You've gotta make decisions.
And who's to say if you're correct?

Join the group or go on your own.
The payoff's better when you're alone,
but that would be mean,
that would be mean.

They say all the world's a game,
and all the people merely players
anticipating what comes next,
but we cant all be soothsayers.
Make a move with what I know, with imperfect information
an asymmetry that leads to my theory's refutation.

You gotta make decisions.
Will you coöperate or defect?
You've gotta make decisions.
And who's to say if you're correct?

Join the group 'cause that would be nice.
Being selfish would pay off twice,
but that would be mean,
that would be mean.

Now let me tell you about a little game that works on the principles of game theory. It's called Rock Paper, scissors, rock, paper, scissors, rock, paper, scissors. And that's the way it goes. Paper covers rock, rock breaks scissors, scissors cut paper, and now it's your turn.

Join the group 'cause that would be nice.
Being selfish would pay off twice,
but that would be mean,
that would be mean.