Ben: So are you ready?

Liz: I'm ready.

Both: Rock, paper scissors.

Ben: Okay, okay, paper beats rock.

Liz: Oh no,

Ben: I'm up. I'm Ben Klemens.

Liz: Hey, I'm Landau and this is Pod, Paper, Scissors.

[Theme music. You've gotta make decision.]

Ben: So this last week, you talked about your your dating life in LA. So I guess I'll talk about what I was doing in LA, which was grad school studying Nash equilibria.

Liz: Oh, that's right. You were over at Caltech.

Ben: Yeah, I was enjoying the beautiful sunlight from inside of classrooms. And while I was there, you may remember the movie, A Beautiful Mind came out.

Liz: Yeah, well, you were at Caltech. I was at Princeton, where John Nash did his influential work.

Ben: Uh, That's great, Liz. I don't know, I don't know how to recover from your name dropping. [Liz laughs] But anyway, so he, the movie, a Beautiful Mind, was a favorite among the Game Theorists. Because there's only one actual scene of game theory. It's mostly just a biography. But that one game theoretic scene where Nash has this epiphany about what game theory is, is _completely wrong_.

Liz: Oh, right, where he's in the bar with the girls and everything. It's also kind of sexist.

Ben: Yeah, yeah. Well, oh, sorry to cut you off. But we'll have to push this to another episode.

Liz: Yeah, you know, it's one of my regrets in life. I rode a bus with John Nash once and I kind of wanted to be the person to be like, so Dr. Nash, what did you think of a Beautiful Mine? But I knew that I would be like the 10,000th person to ask them that question. So I never did.

Ben: Yeah, maybe Mr. Nash would just have a flyer that he could just pull out like, yeah, here, just read this. I'm gonna go back to reading.


Liz: Don't you mean _Dr._ Nash?

Ben: Oh, right. Yeah, because he wrote a dissertation, he got a PhD. The dissertation, by the way, was something like 17 pages long,

Liz: 17 pages. I was writing 17 page papers when I was a freshman.

Ben: Yeah. So the story I'm told is that the big problem that the dissertation committee had, which I think I may have read in the book _A Beautiful Mind_, the dissertation committee, their question was like, can we actually award a PhD for a 17 page dissertation? Like, what, what does it mean? But I guess it's good that they did, because in the end, he also won a Nobel Prize for that dissertation. It didn't do a lot, because it was 17 pages. What it basically did was it demonstrated that there's this class of things, "games", where there's always this thing, "the equilibrium". So any game that you give me, that's, you know, reasonably well defined, we can find the equilibrium.

Liz: So when you're talking about an equilibrium, you mean, a state in which both players are happy with the outcome of their decisions and wouldn't change?

Ben: Yeah, that's, that's a really great definition, thanks. The problem is that your definition is, you know, extremely sensible, and what we're going to talk about here. The definition in the paper is, you know, we apply Brouwer's fixed point theorem to this class of payoff tables, and we get the following equilibria. And we're not going to go into fixed point theorem on this talk. But the point is, that there's this shear between the theory saying yes, there's always an equilibrium. And the reality of whether people would actually, you know, play that equilibrium. Is it actually a predictive theory that says, This is what people are going to do? Or is just, I don't know, this theoretical construct?


Liz: Alright, Ben, well, a lot of people out there, including myself don't really know about this eyebrow tweezer fixing thing.

Ben: Brouwer's fixed—Okay, okay. It's not important. [Both laugh]

Liz: But okay. Why don't we talk about how it actually applies to real life?

Ben: Sure. Let's do an example. Let's do an example.

Liz: Okay, so when you were talking about finding the equilibrium between two people, you know, kind of playing a game, I thought about how there was this one time in Pasadena, where a friend of mine was going to host a poker tournament at his house and he emailed six people. And two of the six were myself and somebody that I had dated, kind of recently broken up with on not so great terms.

Ben: oooh, So the "Can I go to a party with my ex?" problem.

Liz: Yeah. And it's worse than going to a party with your ex. Because if it's just a house party, you could stay in the kitchen if he or she or they are in the living room. However, if it's a poker game, everybody is in the same room at the same table, possibly making eye contact the whole time.

Ben: Oh, yeah. And it's only worse if it's strip poker, right?

Liz: We don't do that at Caltech. [Ben laughs]

Ben: Okay, though, once—since we're talking about Caltech, yeah, we did actually manage a game of strip Jenga among the grad students once that that was, like a proud moment of having personality. Enough about Caltech. Let's go back to strip poker with your ex. [Liz laughs] So you're what are the options for you and your, your ex? So one is that your ex goes, and you stay home? So does that sound like an equilibrium to you?


Liz: Yeah, if he went to the game, and I stayed home, which actually is probably what happened. I think that's a great outcome for both of us, because I would be happier staying home if he went, and he would be happier going if I stayed home.

Ben: Okay, so that's, that's all very reasonable. So knowing what he did, you're not going to change your mind. And him knowing what you did, he's not going to change his mind. So that it would work this the opposite way, too. Right. So if you went, and he stayed home, that would that would be symmetric, yeah.

Liz: I think that would be totally fine as well, because then he could do whatever he wanted at home. And I would be with the rest of our friends in a safe and jovial situation.

Ben: Great. And so the we have two more possibilities, though, right? Which—These is time for a musical Sting, dun, dun, dun. So one is that you both show up. Right?

Liz: Right. And so if we both show up, again, it's kind of hard to give a polite excuse to leave after 20 minutes or something, if it's a poker game that you consented to be part of. So yeah, basically we we would be kind of like awkwardly at the same table for a long time.

Ben: So there would be regret.

Liz: There could be regrets. Yeah,

Ben: especially once—yeah. Okay, let's drop the strip poker thing. So the other, the last last of our little two by two table, if you go, he goes, whatever, is that you both Don't go.

Liz: Yeah, if we both don't go, then, honestly, our friend who had the poker party loses, in addition to both of us, because, you know, it would have been nice to have one of us there. And each of us would have preferred to be there if the other were not there.


Ben: So let me summarize a few points here. So two kind of notable points. The first is that you can have multiple equilibria. Right. So it would be fine, it would be fine and equilibria-ish. If you went and he didn't, it'd be fine if he went and you didn't. Yeah, right. And inside this simple little game that we're that we're making up here, there's, there's really no way to know what's going to happen between those two equilibria. The other thing to kind of note is, I use the word regret several times here. And even if we don't believe that people play equilibria, there's sort of this interesting thing about—like, you can be negative about it. Like if something is not an equilibrium, what does that mean? And I feel like there's always this sense of regret afterwards where somebody says, "Yeah, looking back on this, I think, I think I kind of made the wrong choice here."

Liz: Okay, okay. So that was one example. But how else is this applicable in our everyday lives?

Ben: So, okay, let's try to make this a series by talking about something that we, we talked about last time. [Dangerous=sounding music]

Liz: Oh, the nightmare of my dating life in LA.

Ben: Yeah. That. So in this, this is something that we talked about last time, and I wanted to say, Oh, this is an excellent example of Nash equilibria. But it was too much and we didn't get to that. But we're getting to it now. So let's say we have some fictional dating app for people in LA. What do you want to call it?

Liz: The Stars and Swipes!

Ben: Sounds great. Yeah. So there, we talked about then two types of people. Which I even even then I was like, Oh, this is a good example of Nash equilibria. But I didn't want to talk about it, then it was a little off topic. And but we're talking about it now. Darn it.


Liz: Oh, I didn't edit that out.

Ben: Okay, we had two types of person on the Stars and Swipes.

Liz: Right. And this is a little bit simplistic, but you could imagine that there would be the people who are looking for a long term relationship. And the people who are looking for some short term fun.

Ben: by the way, we at Pod, Paper, scissors, are accepting of everyone's quirks, and have no interest in slut shaming. So we don't want to say that one type is good or one type is bad. But one thing that stands out is that when there's an interaction between the two, and we talked about this a little bit last time, there's there's potential friction.

Liz: Oh, yeah, I felt all kinds of friction.

Ben: That-You—That sounds vulgar. [Liz laughs]

Liz: When you're looking for, let's say, just some fun, tomorrow night, or even tonight, and you go on an app with that intention, then you might clash with people who are like, no, what do you mean, I'm not gonna come over tonight? I've never even met you. Don't you want to get to know each other first? These are two very different mentalities. They're both very valid mentalities as Ben said. But I've been in a situation where people have been extremely forward on these apps, inviting me over as the first or second line in a text exchange. And I'm like, Oh, no, sorry. I'd rather like, you know, go out with somebody who wants to get to know me. And they're like, no, what do you mean? Like, that's, that's great. But don't you want to get it on?


Ben: Yeah. So it would be nice if there was a way to separate them, these two types of interest, right? So imagine that there were, and honestly, there are, but we should fictionalize this. So imagine that there's an app aimed entirely at long term relationships. Okay. So you maybe record little voice clips because this is fictionalized. And we'll call it the Sound of Settling. And then you—

Liz, singing: And then the people swiped and prayed.

Ben: Okay, you can put in the sound of settling musical sting here. And then we're going to have another fictionalized thing for people who who just want to get laid. You should name it. Let's give it a name.

Liz: Oh, how about L Aid?

Ben: That's brilliant. High five Sound Effect? Great. Ah, all right. Yeah, I like that name. Because they in LA there's I don't know if it's still around they there's a new newsletter that is basically for ads for escorts. It's called LA X-press. And my brother loved this because he's like, wait, LAX has its own press. I'm digressing. [music] Now, we've got three different apps, right. And people have the choice of either being on the general purpose Stars and Swipes or they can move. Okay, so while we fictionalize this, let's start trying to do some analysis. Let's say everybody wants an LTR is on the Sound of Settling,

Liz: let's not use acronyms.

Ben: Okay. Everyone wants a long term relationship is on the Sound of Settling. And everyone who has DTF is on L Aid, is that equilibrium?


Liz: Well, it is because everybody is in theory among the community of people that shares their values and has the same strategy. Though wait a minute Ben, there's actually another equilibrium here.

Ben: Yeah?

Liz: One of the problems that I had with some apps out in LA is that they had recently been introduced to LA, and so the membership was actually quite low, like in a single, you know, 10 minutes, I could actually have gone through every single guy in my age group who was in a five mile radius. And yes, I put in five mile radius because if you go more than five miles in LA, it's gonna take you an hour. [Ben laughs] So yeah, if I've exhausted the pool of members in like 10 or 15 minutes, then I'm going to be pretty doubtful that this app is going to be that useful. So if this other app Stars and Swipes has a huge membership pool, I might actually migrate over there. Even though Stars and Swipes would have people both of the long term relationship and short term relationship persuasions, you might be better off in this bigger pool just because there's more options.

Ben: So this demonstrates another—Naw, this goes back to what we were talking about before that you can have multiple equilibria. In this case, we have one equilibrium where everybody separates into different spaces, and one where everybody pools. And notice, by the way, they're both stable. if everybody's on the Stars and Swipes, you're not going to switch to the Sound of Settling. Like you have no regret.


Liz: I suppose under these hypothetical conditions, I would have no regrets.

Ben: Yeah, so we have to have two equilibria. where everybody's at this the Stars and Swipes and is okay with it, where everybody is separated into L Aid and Sound of Settling, and is okay with it. And there's kind of a chasm between these two equilibria. How you go from one to the other is, you know, one of the often one of the great problems. Like if you were marketing for L Aid, this would be your job, how do we jump from one equilibrium to another?

Liz: Wait, Ben, what do you mean, switch from one equilibrium to another.

Ben: So we can picture one world where everybody is signed on to Stars and Swipes and these other apps are barren, nobody's on them. And another equilibrium where people have separated into these two side apps, and nobody is at the Stars and Swipes. So these are both stable alternate universes. And the question is, is there a way? The question, you know, l Aid marketing is thinking through is, is there a way to jump from one alternate universe to the other?

Liz: Well, is there?

Ben: Maybe we'll we'll consider options later. Let's push that for now. But there's certainly no easy answer. And that yeah, this is what the marketing departments are doing, that they're trying to work out, how can we get a new equilibrium where everybody is used to being in one place when they used to be in another?

Liz: Okay, okay. So, as always, we're talking about theory, but people's preferences change. People sometimes think that they're out to find a long term relationship, however, they meet somebody who is a better fit for them for a very short period of time. Conversely, some people, you know, think that they're just out for some casual fun for just a day, a week, something without attachment, and then suddenly they fall in love. These apps are just there to help you meet people. They're not going to reveal to you your inner self. It is a journey you have to go on...with your own heart.


Ben: Whoa, that's deep. Can you can we close with [both laugh] That sounds sarcastic? It wasn't meant as sarcastic. Yeah, exactly. There's more to it than the simple model here, right. And, in fact, the fact that there are so many people on these general purpose apps, that we wind up with one equilibrium that is, frankly, by the theory less efficient than this equilibrium, where people are in separate spaces. It says something about what people's preferences are, you know, it partly says the marketing is great at the general purpose apps, but it also says, yeah, maybe people don't know what they're looking for. Let me close out with the same Miss manners line I read to close out last time. "It is the essence of social flirting that no one—not even the participants—should be positive that anything more was intended than simple enjoyment and admiration." What I hope we've learned from that from this episode, since this is a game theory podcast, we want to be familiar with sort of the theory of, of what an equilibrium is, because that's kind of the core of all of game theory. The fact that that every game has an equilibrium, and that we're never going to have a game where you can just throw up your hands and go, Yeah, I don't know what happens. Mm hmm. That's, that's why it has a name. That's why that's why we have a term "game theory." And it's complicated. There are a lot of problems to how these equilibria work. And so already we've seen that we have situations where there can be multiple equilibria. And we don't know which is going to, which is going to happen, and sometimes there's this chasm between them and we one is more efficient than the other. But we don't know how to get from the less efficient to the more efficient.


Liz: Okay, Ben, so what I just heard you say is that much like in love that's like in relationships, the human heart, there are mysteries in Game Theory people are still puzzling out.

Ben: Yes, like the song goes, my heart and Brouwer's fixed point theorem will go on. So tune in next time on

Both: Pod, paper, scissors.

[Exit music]