Liz: Hey, Ben, remember I was telling you about my roommate, Chellie?

Ben: Oh, I do. That was last episode.

Liz: Yeah. So we were talking about how, when you live with somebody and you share a kitchen, you could just try to free ride off of the other person and never do the dishes. But the other person kind of has control over that situation because they could just not do the dishes either. And then you're in this kitchen standoff.

Ben: Right, the kitchen standoff. That's one of the outcomes from a repeated prisoner's dilemma. The ideal, of course, is that you both do the frickin' dishes every night. But yeah, it's easy to have a situation—We call this defection, right, where somebody fails to do the dishes. And then the next day, you're like, well, tit for tat. You didn't do the dishes, I'm not going to do the dishes. And next thing, you know, everything is broken down.

Liz: Yeah. So that repeated Prisoner's Dilemma situation, that's only if you assume that the situation never ends. But as we all know, all living situations must come to an end, someone will move out or the end of the week, month, etc. And when you have a time limit, suddenly things get difficult.

Ben: I think I've experienced that. But can I interject with a non sequitur, super bad?

Ben: Hi, I'm Ben Klemens.

Liz: I'm Liz Landau. And this is

Both: Pod, Paper, Scissors.

[intro music: You've gotta make decisions]

Ben: Having expressed that, sorry about the non sequitur, yeah, I think I've been there. I've had housemates, and they give 30 days notice, and then everything gets…weird.

Liz: Yeah. Like you kind of don't know how to behave. Especially if you haven't known the person for that long. If it's really good friend of yours, and you know that you're going to see them all the time anyway, might not be so strange. But if your relationship is purely as cohabitation, and then that habitation is ending. It's like, well, do I still care about the dishes?


Ben: So this gets tested in the lab. This is a well known sort of game. It's called the centipede game. Last time, I called it the caterpillar game, but that's longer. Centipedes, they only have 100 feet.

Liz: Wait, does this have to do with that, like really nasty centipede thing that there's a South Park episode about?

Ben: Do I want to hear about this?

Liz: No, it's it's not suitable for young ears.

Ben: Okay, well, well, we'll just let the people who know what that's about wink with you about that, but okay. No, it's Game Theorists, so they have no sense of humor and it's all very boring. But yeah, so the centipede game, it's, it's much more boring. So you and I are going to have some sort of Prisoner's Dilemma interaction. So you have an incentive to defect to take the money and run. But if you don't defect, then you're going to have another period where we play the game again. So it's called the centipede because it—Okay, the head of the centipede we just met, and we're about to start our first game. The game can go forward, that's the version where we coöperate, or it can go down, which is when one of us defects, if it goes down, the game's over. If it goes forward, and we coöperate, well, you have the option to defect and it goes down. And then that's the end of that thread, or it goes forward, and then you have the option to go down. And hopefully, I'm painting the picture of this long chain of things, where each step, there's this down option where the game just ends. And in the lab, they'll play this for 100 steps, which makes it a centipede.

Liz: Wait, what does this have to do with my housing situation?

Ben: The thing about the centipede game, it's only 100 steps. So it ends.

Liz: Oh, so like, step 99. You know, it's gonna end at 100.


Ben: Yeah, so at 100 What are your incentives? Well, it's a simple one shot prisoner's dilemma formula, the only equilibrium in a in a one shot prisoner's dilemma is for both people to say, I'm not watching the frickin' dishes, you do it.

Liz: So on day 99 I'm just thinking about on day 100. Just one day from now, I know that Chellie won't clear the table, and she knows I'm not going to do the dishes. So why would I do the dishes on day 99 when she won't coöperate tomorrow, no matter what I do?

Ben: Sounds about right. If we know there's going to be mutual defection on day 100 no matter what, what is there to plan forward to on day 99.

Liz: But then day 98 you know that that day 99 is coming, and then they have 100, and therefore, you should defect.

Ben: I suppose so. If you know that someday, that you're not going to get coöperation next period. Why wait for next period? Why not just defect now?

Liz: But we then we could just keep going backwards in time. 97, 96 95, basically, all the way back to day one.

Ben: You could, this is known as backward induction. Right, you started at the end, and you sort of worked your way backward. And we've just proven that the only thing to do in this sort of theoretic perfect world is that you on day one, you say, well, someday, things are gonna fall apart. So I might as well just stop now.

Liz: Wait, so that means that when you move in to a new house with roommates, you might as well just be a jerk and never pitch in around the house and never clean up, etc.

Ben: That's the theory. That's the theory. And of course, that doesn't actually happen. If it does happen, yeah, you're in a bad way and you you gotta you got to get out fast. But yeah, in reality repeated prisoner's dilemma is work.

Liz: So repeated prisoner's dilemma is what we were talking about last time where there is no end in sight, and you just coöperate so that the other person coöperates, right?

Ben: Well, this is still a repeated prisoner's dilemma, you do repeat the prisoner's dilemma 100 times. But yeah, if there's a set ending, you get a different result than you get if theoretically, you go to infinity. But the result we see IRL is closer to that thing where you go to infinity, then the result where yeah on day one, you're like, well, this will all be over soon. So I'm just going to be a jerk on day one. So I guess the question is, you know, there is no infinity in real life. So why do people coöperate?


Liz: It must be love, then it must be love.

Ben: Well, that's one story there. People are just nice to each other. And Game Theorists, they're, you know, an offshoot of hyperrational economics. And economics evidently attracts a lot of people who are evidently jerks and are like, yeah, you know, I would just defect on day one, if I had the option. And now it's a mystery. It's a total mystery why people coöperate. But yeah, I think we can be a little more rational about it to some extent, and try to think of other ways in which people might coöperate. Like, really, if you know that your opponent will coöperate for at least some number of periods, like for whatever reason, they they showed up drunk, and they couldn't work out the optimal equilibrium. Or really, it really is love. Who knows what.

Liz: What about sea urchins? [laughs]

Ben: Yeah, so in in doing the minimal amount of research that we do for these, these talks, I picked up a book by Ken Binmore. And he had, like, several pages of narrative about this. So if you don't know Ken Binmore. I knew him briefly. He liked—

Liz: no one knows him.

Ben: Well, I can I tell exciting anecdotes about—

Liz: What I've learned about podcasting is that no one cares if you've met an obscure person that you think is important. Okay, with apologies to Mr. Binmore. But we must move on anyway.

Ben: In the end, we set fire to my dissertation. So yeah, he gives this one example, he talks about how when he was a kid, he wondered why when you go to the go to the convenience store, and you buy—you hand over money to buy, like, I don't know, whatever, what do kids buy, cigarettes, and you hand the money over, why does the shopkeeper even give you anything? You can just say like, Alright, thanks. Get out of here. And of course, the fact that he was a small child and he started thinking this, he was destined to be a game theorist. But it happens, right? They will give you the cigarettes, what would happen if they didn't?


Liz: Well, then you would go on Yelp. And be like, this is the worst store in the world. They keep your money, do not go there. And then no one else would go there.

Ben: Even pre Yelp, reputation got around. And so even for for Ken Binmore buying his cigarettes, yeah, it's better to have him hand over the money every every week, or I don't know, if can be more of the 12 year old was a chain smoker or something.

Liz: Smoking is bad kids don't do it.

Ben: You get it, you would rather repeat the interaction than to just cut it off. And we see this, this happens in real life. And then Binmore went on to talk about drug dealers. And it's interesting that he brings up drug dealers because they, you know, I've seen The Wire. Drug dealers are famously—

Liz: when you walk through the garden,

Ben: they're famously unscrupulous right? It's not because they the dealer loves the buyer or the buyer loves the dealer. He then gives the example from street urchins to sea urchins. Sea urchins are hermaphroditic and one will lay eggs and the other will like care for the, the other sea urchin will care for the eggs

Liz: for a while. It's like sharing responsibility.

Ben: Yeah. And then the other one will lay the eggs and the first one will care for them for a while. And yeah, it's a repeated prisoner's dilemma. Every period on sea urchin has the chance to shirk, and be like, Nah, now you take care of the kids. I don't care.

Liz: So it is like evolutionary game theory,

Ben: I suppose so, because they continue to exist and live and stores continue to exist and whatever stores are like no screw it, they're kind of gone.


Liz: Well, yeah. And like if I hire a babysitter that I would use in the future. And she takes my kid and drives him to New Mexico and has to go and find them. Well, guess what? I'm not going to use that babysitter again.

Ben: Totally. So we have we have a good number of examples here of repeated Prisoner's Dilemma those were coöperation actually happens: so the shopkeeper gives over the stuff, The drug dealer gives over the stuff, the sea urchins share, babysitters don't drive the kids away to New Mexico. And then you know, I guess you can ransom the kid for like millions of dollars.

Liz: What if you have a summer fling, you know that you're never going to see this person again, because you're just spending the summer in Sevilla. And on the last day, when you're saying goodbye at the airport, you grabbed the dude's wallet, and you get on that plane to the U.S.

Ben: You did this, didn't you? That you're speaking from real life right.

Liz: Now I'm not saying I didn't do it. But I'm not saying I did. I'm just asking what is stopping me from doing so.

Ben: Well, you just never know in life if you're going to meet somebody again, yeah.

Liz: that's true. I mean, 15 years later, I might be hiking the Dolomites. And then there's Pablo, and he's like, tú me robaste el dinero. Dame el dinero.

Ben: Right, and you're on a mountaintop and he just like pushes you over.

Liz: Yeah, hashtag retribution. So I guess we all better be nice to each other, because you just never know. Back to the roommate example.

Ben: Yeah, he By the way, when we rehearsed this, Liz asked aren't all endings probabilistic? I guess I'll just steal it. Liz aren't all endings probabilistic?

Liz: They are. I've been thinking a lot about this because, you know, Chellie is moving out, and it's very likely that we will never live together again. However, let's say that Chellie applies for a job at the place where I work 10 years from now, if she leaves a bitter taste in my mouth, with her failure to clean up the kitchen, am I going to recommend hiring her 10 years from now? Perhaps not.


Ben: And you know what, there is some some overlap in social circles, there's going to be some chance that word gets around. In the centipede game getting better, this sort of perfect theoretical thing, round 100 there is an ending and that's it. One thing that people do in, in the theoretical game is when they set up the game, they say, okay, every period, you're going to play this, and there's some chance, you know, one in 30 or something that I'm just going to cut off the game, you're gonna play and then instead of saying, Alright, next round, I'm just gonna say alright, game's over. And people are much more likely to coöperate, because they don't see the ending. They don't have to worry about well, in the next period, my opponent's going to defect.

Liz: Yeah, so even if Chellie gives 30 days notice to move out, you just never know if that's really the end of your interaction with that person.

Ben: There's another thing that I've been sort of reading about and thinking about, that may explain this sort of unwillingness to backward induce from 100 steps forward. And it's called the unexpected hanging.

Liz: The unexpected hanging!

Ben: You didn't expect that did you.

Liz: I did not.

Ben: So the paradox of the unexpected hanging, I first learned about it from Martin Gardner. Is it okay, if I read to you from his book entitled, The Unexpected hanging?

Liz: Martin Gardner You mean the Scientific American columnist?

Ben: Yeah. And this was almost certainly a Scientific American column before it got anthologized into the book. He traced back the story of the unexpected hanging. I'll read it. Leonard Ekboom, who teaches mathematics at Östermalms college in Stockholm, pinned down what may be the origin of the paradox in 1943 or 1944. The Swedish Broadcasting Company announced that a civil defense exercise would be held the following week, and to test the efficiency of civil defense units, no one would be able to predict, even on the morning of the exercise, when it would take place. The weird thing about it, let's say the week ends—when do weeks end, Sunday? Okay. Sunday rolls around, and they said you wouldn't be able to predict that the exercise would take place, but Sunday morning you're like, well, it has to be today.


Liz: But wait a minute, Ben, if you think, okay, it's Sunday, then you won't be surprised. So you work backwards.

Ben: Yeah. It can't be Sunday. I won't be surprised.

Liz: And then you think about Saturday. If you think that it's Saturday, then you won't be surprised then either.

Ben: Knowing that Sunday is off the table, it can't happen Sunday, It can't happen Saturday, because Saturday morning, I'm gonna be like, well, it's not tomorrow.

Liz: And then you just go all the way back through the days of the week, and then you're like, well, I won't be surprised any of these days.

Ben: Exactly. So we've just proven that the exercise can't happen.

Liz: But then the exercise happens on Tuesday. And you're like, oh, that was unexpected.

Ben: Exactly.

Liz: But not surprising.

Ben: Exactly. Having set up the logic, and having proven that it's impossible on every day, well, it's possible on any day, you know, the author notes that even on Sunday, you'd be pretty surprised. And yes, so much has been written on this.

Liz: Well, I guess the explanation that I would give Ben, is that if you talk yourself out of it, if you say, this thing definitely won't happen any day this week, and then it happens on Thursday, then you are surprised because you've put yourself in the mental state of this definitely will not happen.

Ben: Yeah, if you've ruled out all the possibilities, and all the possibilities are, in the end, equally likely, equally possible.


Liz: But wait Ben, you called this the unexpected Hanging. Are you saying somebody's gonna get hanged in this example?

Ben: Yeah, there's a version where the storyline is that there's a jailer telling a prisoner that they're not going to know what day they get hanged on. And yeah, I don't know what it means that theorists gravitate toward like, prisoners in interrogation rooms or people getting hanged.

Liz: But in the civil defense version, or the unexpected hanging version, or the centipede game, they all have that same backward induction where you can step backwards from the last day all the way to the first possible day to say something about every other day. I guess you don't need criminals for that.

Ben: Lemme just note, before we close out this unexpected hanging section: when I think about this stuff…my head hurts.

Liz: Oh, so it's not just me.

Ben: Yeah, this stuff is really hard to think about, and I think the lesson we get from that is that backward induction is not natural. It's not something that we as people are used to, and if you have a centipede game, it's not guaranteed that people are going to think back the way that we were able to think back here.

Liz: Well maybe we should just be nice to each other, Ben.

Ben: I guess that's a possibility.

Liz: And you know, it's even like listening to this podcast, well, it sounds in their voices, like this is gonna wrap up soon?

Ben: Yeah. And you know, we talked about in this episode, how the prisoner's dilemma, this repeated prisoner's dilemma, one way to maintain coöperation is that there's sort of a probabilistic ending and you're surprised when it e—