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38: The Great Stratagem Heist (Game Theory: Iterated Elimination of Dominated Strategies)
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Game theory is all about decision-making and how it is impacted by choice of strategy, and a strategy is a decision that is influenced not only by the choice of the decision-maker, but one or more similar decision makers. This episode will give an idea of the type of problem-solving that is used in game theory. So what is strict dominance? How can it help us solve some games? And why are The Obnoxious Seven wanted by the police?
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Transcript
Introduction to Game Theory
00:00:00
Speaker
Game theory is all about decision making and how it is impacted by choice of strategy. And a strategy is a decision that is influenced not only by the choice of the decision maker, but one or more similar decision makers. Today's episode will give an idea of the type of problem solving that is used in game theory. So what is strict dominance? How can it help us solve games? And why are the obnoxious seven wanted by the police? All this and more on this episode of Breaking Math. Episode 38, the great stratagem heist.
Sophia and Diane's Episode
00:00:32
Speaker
I'm Sophia, and filling in for Gabriel is my mom, Diane Baca. Thanks for being on the show. You are very welcome. So today we're going to be talking about game theory, and you listened to the previous episode, so do you want to give a recap based on what you understand? Oh, that'll be interesting. Okay, yes. This is a test for breaking math.
00:00:52
Speaker
The hard part about this is that I, of course, am not super knowledgeable about game theory, so this is going to be fun. From the last episode, I gathered that game theory is about making decisions based on whether it's advantageous to you and possibly advantageous to the group, but basically you make your decision always in your favor.
00:01:17
Speaker
It's a logic puzzle and you are weighing the choices always. And in that weighing of choices, I guess if you're doing game theory you can
Mathematical Decision-Making in Game Theory
00:01:27
Speaker
compare two people. One is you compare their two choices and together you look at which one mathematically would end up being the best choice for the move that you're going to make.
00:01:39
Speaker
Is that okay? Yeah, that pretty much sums it up. We went through a few different strategies with Broken Lego, the person who was part of our Saw parody. Oh, and before we go on, I should probably mention that my mom taught me math, so she's the reason for breaking math.
00:01:59
Speaker
I'll take that credit. Thank you so much. Just kidding. I did teach you math. Long time ago. Oh my god. Yes. I'm a math teacher, but I think I taught Sophia algebra when she was in third grade. And so one thing that really, and this is part of Breaking Math's mission and part of this episode, of course, is that being good at math is all about installing intuition in the right places in the mind.
00:02:24
Speaker
basically tuning your intuition into what something is, getting a sense for what division is, everything like that. And that's what this episode is going to be about. It's going to be about mostly one problem that's going to be solved. And we're going to just go through that in great detail.
00:02:44
Speaker
All right, so we're going to talk about strict dominance. But before we have to talk about strict dominance, we have to talk about what a strategy is. In a strategy, I think we mentioned, I'm not sure if we mentioned in the last episode, did we mention that, or do you remember about strategies? Did we define that well?
00:03:03
Speaker
No, I don't think you did. I think it was more about just the logic of the choices. And you did mention one thing about the one-liner, about the strategy being always in your favor. That's the definition of dominance. See, a strategy is a decision based on the idea that other people can make their own decisions. So like in a game, you know, the other person has freedom. And usually the point of a game is to, in game theory, you always want to maximize some value.
00:03:31
Speaker
And that's how a game is defined mathematically. It has to be able to be maximized. There has to be a strategy is better than another. One of the things that I was a little bit, um, or I thought was unusual about the whole game theory thing. And it feels very real, but at the same time, um, when you're talking about the prison situation, um, it's like they knew each other and then they could cooperate.
Selfish Behavior and Competitive Games
00:03:53
Speaker
So they had a lot of trust. So I feel like when you're really playing a game, you are always playing against an enemy.
00:03:58
Speaker
Yeah, and maybe that wasn't explained very well in the episode. We were trying to make it so that it was just some random other criminal that might have done something horrible you don't know. So it wasn't supposed to have any prior knowledge, but we didn't explain that well. So in game theory, you're always assuming that the other person is going to be extremely selfish and do the best thing for themselves.
00:04:19
Speaker
Even in cooperative games, which you mentioned at the beginning, the difference between working together and just being separate entities, there was a theorem proved by John von Neumann that said that you could always make a cooperative game into a competitive game or vice versa by removing or adding a player that is worth the total value of points, but that's a little, I think, more out there. We're not going to cover that on this episode.
00:04:41
Speaker
Well, I just was thinking with the prison thing is that if they were both friends and they could figure out the logic, it'd be very simple to figure out that if they both just pleaded guilty, that they would only get one year. But in the end, they end up with a five-year sentence, right? Yeah, and I'm kind of wondering, because I'm very new to game theory myself, I'm kind of wondering how that would be represented, because I know cooperation is... I don't know how to...
00:05:03
Speaker
Model statistical cooperation like the probability that someone will help you and how to factor that into your decisions If somebody listening knows that breaking math podcast at gmail.com only plug our other stuff our patreon is patreon.com slash breaking math podcast we're at breaking math podcast comm and we're on Facebook at facebook.com slash breaking math podcast and Twitter at breaking math pod and Yeah, I think that's all I things
00:05:27
Speaker
So a strategy, of course, you know, it's a decision that you make based on other people being able to make decisions. So a strict dominance of one strategy over another is when the dominant strategy is better, no matter what the other person does, than the strategy over which it dominates. Does that make sense?
00:05:44
Speaker
Yeah, I think that makes, I mean basically it's saying no matter what they do, your strategy is always going to be better. No, how would I say that? If you have choice A and choice B, like if you could either do A or either do B, if A is better in every case, no matter what the other person does, then you choose A over B every time. So that means A is strictly dominant over B.
00:06:04
Speaker
Right. So in the case that you were talking about, yeah, okay. It always was better if they both cooperated. I can't remember the word you guys used for it, but yes. Yeah. And what's interesting about this is that if you have, if you have, let's say I have three options and you have three options. If you have one option that is always better than another one that is strictly dominant over another one, you could basically get rid of that other thing as a possibility for yourself.
00:06:31
Speaker
the other option. Yeah. Yes. That makes sense. Yeah. So if you imagined a grid with rows and columns where the rows are my decisions and the columns are your decisions, then you could imagine this as kind of taking out rows and columns. So if I, so in, this is actually a method which you can use to solve games. And there's, we're going to go over a storytelling example.
00:06:57
Speaker
Well, I think that thing you actually tried to show me this. So we're sitting in a coffee shop last week and she was trying to show me the logic in the visual representation of it, which is a rows and columns in a matrix. And for me is a little tough, but I part of the reason why the story came about is because it's like I mean, since this is a podcast, it's so much easier to understand audibly, right? Yeah, you could hold a story in your head, but you can't hold 18 numbers in your head very easily.
00:07:26
Speaker
Right, and the whole thing with the rows and columns can get pretty complicated. Yeah, because remember three rows, three columns times two, because there's two players. So for each one, there's two different values you have to consider. And to recap, the value of a decision, it's basically a thing that allows you to decide what is better than another decision. So you don't care about the other person's points, you only care about your own points.
00:07:49
Speaker
So the other person could have like a million points and you could have two, but you could have, that could be your best strategy and it could even be qualitatively better. It doesn't matter how it's represented. So it's not a matter of numbers. We're not comparing numbers of each player. We're just playing, comparing the numbers on each player's options. Yeah. Their own numbers. Yeah. And their own possible moves.
00:08:08
Speaker
The story of the Obnoxious Seven The criminal game, The Obnoxious Seven, are a gang of five people, told you they are obnoxious, who've sworn an oath of allegiance to one another and, except for the spineless head honcho, would never crack under interrogation. The police only care about getting as much evidence as necessary to bring The Obnoxious Seven to justice, will arrest any they find just in case, but they expect no information from them.
The Obnoxious Seven and Police Strategy
00:08:35
Speaker
All right. So, um, we have our two players first. I'd like to thank you. Thank you for making the obnoxious seven made up of five people. So I constantly have to fix that in my brain, but that's okay. They're obnoxious. Keep going. Oh yeah. So yeah, I mean, they have to be obnoxious. Um, so we have our two players, right? We have five players, right? What I mean is we have our two kind of actors in the game theory thing. We have the police versus the criminals.
00:08:59
Speaker
Okay, gotcha gotcha. Yeah, those are players and Remember, they're against each other. This is a little more simple than the than the saw episode Because they're obviously against each other right right and the police have their own actors as we shall soon see that are Related to the decisions that they make so remember These are actors that are gonna make a decisions and he shall see soon
00:09:22
Speaker
The Obnoxious Seven are suspected of robbing gems from a bank. There are only three places that are nearby to hide in. The restaurant, Les Knob, The Pier, and the Salsa Factory. Salsa Reno. The five of the seven hacked phone signals and wires and such around the bank, so there was no alarm. And so the police have responded after the Obnoxious Seven and even some witnesses have left the scene and gone back to their business.
00:09:50
Speaker
The obnoxious seven do this kind of thing on the reg, so people have kind of a shrug it off attitude towards crimes. The police can either send in Sandra, the detective, Pete and Tom, the patrol officers, or a SWAT team just itching to make arrests.
00:10:06
Speaker
All right, so let's go over the options. So we have a restaurant, right? Yes. A pier and a salsa factory. So just to kind of build this scene in your head, the pier is next to, of course, the ocean. It has a bunch of games and carnival stuff on it, whatever.
00:10:21
Speaker
The restaurant, it's kind of obviously a little noisy place, really busy, lots of people. And the salsa factory is also very busy, but it's also kind of a dangerous place, a very chaotic place, because it's a factory. Like can you imagine if they hit out in the salsa factory? That would be chaos. So those are the three choices for the obnoxious 7, right? The five of the obnoxious 7 have three choices.
00:10:43
Speaker
Yes, they have three places to hide and then the police have three options to send in. Yeah and their options are what again? Detective Sandra. I like that she's Detective Sandra by the way. Okay patrol officers Pete and Tom and of course a SWAT team. So it seems like we have a varying degree of the level of enforcing here. We got one person, two people or a whole SWAT team.
00:11:05
Speaker
Yeah. And not also remember that the detective, she has certain advantages. Um, like she might know how to gather information better than the patrol officers. The patrol officers might, um, know the obnoxious heaven better and the SWAT team obviously has more brute force, but they're more blunt about what they do. Got it. No. Yeah. I could totally get that. So we have different choices. That's the whole point. Yeah. So, uh, now we're going to go over what happens in every situation. So, uh, hang tight.
00:11:35
Speaker
So now we're going to go over what happens in the snob, the fancy restaurant.
00:11:45
Speaker
Suppose the seven hide out in the snob, the fancy restaurant. Inside it is noisy and crowded. Detective Sandra won't be able to find the criminals, especially since she doesn't know any other faces, and the criminals will walk out the front door with cash. She will be able to round up a few witnesses though. The patrol officers Pete and Tom will be able to arrest a couple of the people that they recognize, but for the most part,
00:12:07
Speaker
But the most they'll get otherwise are a few scant clues dropped by the criminals. The SWAT team would alert the criminals to the presence of the police so they'd be able to sneak out the back with a vase. The likelihood that the criminals would drop damning evidence in their HD escape though would be very high and so the police would have proof.
00:12:27
Speaker
So let's go over that. Uh, what did you, what's your question? So basically Sandra has, I mean, each one of those things has an advantage. Okay. And we also are assuming some kind of action on the part of the criminals, right? So if Sandra goes into the restaurant, okay, the criminals, it's assumed that they're going to be able to walk up the front door with cash. So not only had they stolen gems, now they're going to be able to steal cash from the restaurant.
00:12:52
Speaker
Yeah. And so just to make this a little more mathematical for everybody, the criminals have four different levels of four different things that can happen to them. They can steal some cash, which is the best option. That's that's the best thing that the criminals can do. That's like the best outcome. We are already assuming that. So in other words, they stole the gems, but now they're going to go steal some cash from somewhere else. And now they have both liquid and OK. Gotcha.
00:13:19
Speaker
Definitely, yeah. And that brings us to our next thing. The second best thing that could happen is that they steal something that they can sell. So not steal cash, but steal a vase, like we were just talking about. So cash is the best, something else, the vase is next. Okay, keep going. The best thing that could happen, which starts to get bad, is that some of the foot soldiers from the criminals get caught. Okay. And remember, the foot soldiers don't talk to anybody, so they don't help the police make arrests, which is important. Okay, foot soldiers, does that mean one of the five, couple of the five?
00:13:47
Speaker
Yeah, a couple of the five of the obnoxious seven who have three choices. Okay, got it. Okay, and then the last choice is that they all get caught, I assume. That's the worst thing that could happen to them. Yeah, well, the worst thing that could happen is that some foot soldiers, because some always get away, but the worst thing that could happen is that they lose money and they get caught. So the ones who are carrying the money from the, or the gems get caught.
00:14:10
Speaker
Okay, gotcha. Gotcha. So if foot soldiers get caught, are we assuming they don't have any gems or cash or vase or anything on them? Yeah, the worst is that the one with the stuff gets caught. They all get caught. Okay, got it. Okay. So now let's look at what can happen for the police. The best thing is that police get some really important proof, something that will definitely make the case. Okay, something to convict them. Like they get all their identities or something. Okay.
00:14:39
Speaker
yeah the second best thing that could happen is that they get some witnesses some witnessed uh some witnesses who are at the bank that they stole the gems at wait wouldn't the best thing happen that could happen be that they caught them all uh but that won't happen they never do they spoiler alert
00:14:55
Speaker
Oh no, they never get caught? No, at least one gets away. Okay, nevermind. Oh, at least one gets away. So this is an assumption of the game then. That's the important thing about game theory is that you're assuming, I mean, at least in this thing, you're assuming that you know all the outcomes and you're assuming that the other person knows all the outcomes.
00:15:12
Speaker
okay okay is this similar like in chess to say that when you make a move you know that they're gonna die kind of thing oh yeah so that's like the difference between chess and poker is that chess you know exactly what the other person can do yeah and what the outcome will be if they do it so this is more like a chess situation like we understand exactly what the options are basically
00:15:34
Speaker
yeah versus poker where there's random cards so helpful for me personally okay gotcha yeah i keep thinking of clandestine situations like oh i have no idea what's happening okay gotcha okay yeah and by the way the court case after is not part of the game so they might catch them later based on the proof or whatever
00:15:53
Speaker
Okay. Gotcha. Okay. So we didn't go through the four cases. I'm sorry. I distracted you, but here we go. So, yeah. So the third best thing is that just some scant clues are found and the last and the worst thing would be that, uh, they destroy the evidence or bundle it. Oh, okay. Okay. Gotcha. Or don't find any evidence. Oh, they never don't find evidence. Spoiler alert too. So they always find evidence, but the worst case scenario is that they botch it.
00:16:21
Speaker
Yeah, so just to go over the criminals one more time, they either steal extra money, just steal something to steal, they lose some of their foot soldiers, or they lose their money and their foot soldiers. And for the police, it's that they, the best thing is that they find some proof. The second best thing is that they find some witnesses who can give witness testimony. The third best thing is that they find some scant evidence. And the fourth best thing is that they bungal some evidence. So those are the four rankings.
00:16:50
Speaker
And by the way, you don't have to remember what happens in every case. We're gonna go back over it, but we just want you to have an idea of the narrative.
00:16:59
Speaker
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00:17:28
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00:17:55
Speaker
Now suppose the seven hide out around the pier. The pier is where the detective Sandra does a lot of her work. If she goes to the pier, she'll probably be able to recognize the suspicious behavior typical of people like the robbers among the people around that open environment and arrest the ringleader and probably even extract a confession.
00:18:14
Speaker
The pier is so wide open, though, that Pete and Tom would be more visible to the criminals than vice versa. And so the criminals would be able to hide in one of the prize booths and leave with a bunch of stuffed animals as loot. But they would be able to find some witnesses to the crime. And I just want to interject here that this is the second best option for the criminals because they leave with the stuffed animals that they could sell. I remember this option too. And the police, though, it's also optioned over them because they would be able to find some witnesses to the crime.
00:18:42
Speaker
and remember the only better thing is absolute proof. Okay, and the SWAT team would be able to, through sheer numbers and with a flanking attack, be able to arrest a bunch of foot soldiers, including the ones who were carrying the loot from the bank. Worst option for the criminals, but keep going. But it's very likely that the SWAT team would drop the evidence in the ocean. It's happened like every time before.
00:19:06
Speaker
So also the worst option for the police. Okay, so we're just going over the strategies for place by place now, but then we're gonna go over person by person, the people that the police send in. And as you'll see, the police have one strategy that's strictly dominant.
Detective Sandra vs. Patrol Officers
00:19:31
Speaker
Finally, suppose the seven hide out in Salsa Reno, the Salsa Factory. In Salsa Reno, Detective Sandro will be reduced to finding some scant clues as the criminals abscond with the loot and also some jars of precious salsa. Sorry, I'm thinking, oh, this is definitely a New Mexican story.
00:19:48
Speaker
Yeah, no, it's not green chili. Oh, that's true. It's okay. The green chili factory. No, we're retconning it. No, it's green chili side. Okay. Yeah. It's green chili side. Yeah. We drink with our Coke Pepsi. I know. Right. Our Pepsi Coke, Albuquerque jokes.
00:20:05
Speaker
Yeah, remember this is because the factory is very busy place Detective Sandra is It's good at her job But remember the criminals are running and they could go through hallways and all that second best option for the criminals They find the salsa but a third best option for the police. They only find clues
00:20:22
Speaker
Okay, continuing. If the patrol officers Pete and Tom are sent in, they'll be able to arrest some foot soldiers. But since they don't really have the authority to shut down Salsarino, it's likely that in the pandemonium, they will ruin the evidence that they have. Obviously that is the worst option for the police, right? Well, no, they did arrest some foot soldiers. So that's good for them. But they bungled the evidence. Oh yeah. Okay. So, uh, that is the third best option for the criminals, right? The arrest. So basically this is a pretty bad option for both of them, but keep going.
00:20:51
Speaker
If they send in the SWAT team, however, they will be noticed by all the workers, which will likely include someone who is at the bank, who can be interviewed by the police and the police will arrest a few foot soldiers. So second best option for the police, but third best option for the criminals, right? Awesome.
00:21:10
Speaker
So now we're gonna look at the strategies, but from the point of view of the police. So the question we ask now is, what is the best strategy for both the police and the obnoxious seven? Okay, so in the case of this, what we're doing is we're gonna be comparing what they all can do. And we all know, we know all the choices, both sides. The police know everything on the criminal side, the criminal, everything on the police side, correct? Yep. Okay. So they know their hands.
00:21:39
Speaker
Yes, they know each other's hands got it got it Okay, we could show that the detective is a better option to send in than the patrol officers in every case because at the restaurant Okay, so now we're looking at a method okay what we're gonna compare the detectives versus the patrol officers right yeah, and if we compare them the detective is always better than the patrol officers and
00:22:01
Speaker
Yeah, yeah, because if they go into the restaurant, okay, so Detective Sandra goes in, she'll be able to find some witnesses, but the police will only be able to get some scant clues, and witnesses are better than clues, right? Exactly, so in that case, detectives better than police. Alright, yeah, and at the pier, Detective Sandra, she's the one who arrested a ringleader who is spineless, if you remember the introduction.
00:22:22
Speaker
So that is basically proof and the police can only find witnesses to the crime. So that is better in that situation. Absolutely. And in the last situation, the detective can only find some scant clues, but Pete and Tom actually bungled the evidence.
00:22:36
Speaker
Right. So in every case, detective Sandra is better. So we are going to eliminate Pete and Tom as an option for police action. Exactly. And, um, now it, now there's no strict dominance though, between, uh, now let's look at the detective versus a SWAT team. Uh, can we eliminate one? Let's go through.
00:22:55
Speaker
Okay. So in the first case at less knob, okay. If they send in the detective, of course, she was going to be able to find, um, some, some evidence or some witnesses. And the SWAT team was going to be able to find absolute proof. Absolute proof. Right. So the SWAT team is going to find absolute proof. So that case, the SWAT team is better.
00:23:17
Speaker
Yeah. So Sandra loses. So what about in the pier? All right. So in the pier, the SWAT team arrests some foot soldiers, but remember they bungled the evidence. Right. But then Sandra actually gets the ringleader at the pier. So she's better. Yeah. Okay. So in that case, Sandra is better. So we've already eliminated, we've already.
00:23:36
Speaker
Yeah, so we showed there's no strict dominance there because strict dominance has to be in every case. Yes. Okay. So we're out of options for iterated elimination for the police. Now we got to switch to the criminals options and what they can do. Okay. So, but we're still left with Sandra and the SWAT team. Sandra and the SWAT team on the police side, but the criminals, we don't know what their best option is yet. Okay. So let's go through that.
00:24:02
Speaker
All right, so now we're going to look at what the police can do. And, uh, we remember we don't have to, we're going to compare the list knob, the fancy restaurant versus the pier, but we don't have to talk about Pete and Tom anymore because they're eliminated as a strategy. And we're looking at what the criminals were looking at from the criminal side right now. Correct.
00:24:20
Speaker
Yeah, and remember the criminals know that Pete and Tom are a bad option for the police, so they eliminated them too. Exactly. In the snob, if they send in Detective Sandra, it's better for them than the pier, because they get caught in the pier, but in the restaurant they get out with all the cash.
00:24:34
Speaker
Yeah, that's right. And if they send in the SWAT team, they escape with a vase. The soldiers that were arrested, they're carrying the loot. Also, they get arrested. The pier is actually a worse option for that too. So we can actually eliminate the pier as a strategy altogether. The pier is a bad place for both of them. Okay, so now we're only going to be comparing Les Knob and Salsarino.
00:25:02
Speaker
Yeah. So let's do that real quick. What happens if the criminals go to the snob and detective Sandra goes in? What happens to the criminals? The criminals, uh, get away. Uh, yeah. And they get out with cash. So it's the best option. Yes. Yeah. And, uh, we don't care what happens to Sandra right now because we're only looking at the criminals, the other point of view. Okay. Got it. And so then if the criminals go to salsa Reno and they send in Sandra at the same time, they send in Sandra.
00:25:30
Speaker
They'll only be able to get some salsa. So it's not the best option for them. So It's better to go for the criminals. It's better. They snob. Yeah. Okay. Now let's look at the SWAT team Okay, so if the criminals go into lay snob and they and the SWAT team happens Okay, it's very good for the SWAT team but very bad for the criminals because they get caught. Oh, no, they drop damning evidence Dang it. I miss that
00:25:57
Speaker
Oh, and by the way, just a quick explanation in case it wasn't obvious. The ringleader getting caught is the end of the criminal organization, but getting damning evidence is not the end. It's just the end of them for a while. I probably should have explained that. So that's not considered because they could just regroup with all their loot. They don't get reco'd.
00:26:18
Speaker
Okay. Got it. But still, okay. So if we compare this knob in the case of less knob, the SWAT team would alert the criminals to the presence of the police. So they'd be able to sneak out the back with a vase. Yeah. So, um, and versus in Salsarino, they, uh, would get arrested by the SWAT team. Okay. So in that case, uh, then the, I mean, the, uh, the stop is better if they send in the SWAT team.
00:26:42
Speaker
That's right. So it's better for them in each case, right? Yes. Now one thing is you might think, well, they would drop, they, they dropped having evidence if they go to the restaurant. Yeah. That's part of, yeah. Okay. So that's not, uh, but the reason why that doesn't matter to the criminals is cause they still got the money. The only thing that could destroy the criminals if their ringleader gets caught. Okay. Got it. Okay.
00:27:03
Speaker
But they could regroup even if they find damning evidence is there only a convict like leaders. Okay. So in that case, then let's not is a better situation than Selsarino for the criminals. Yeah, because in every case, right.
00:27:16
Speaker
Mm-hmm, so we can eliminate now. It's all Serena. All right, so we only have two options to consider left to we're down to two the two options is that the seven hideout in the snob and detective Sandra is sent in It remember detective Sandra won't be able to find the criminals because she doesn't know any of their faces She just got sent into this but they'll be able to walk out the front door with cash. So it's the best option for the criminals and
00:27:41
Speaker
It is the second best option for the police and if they send in the SWAT team However, it is they would be able to find the worst evidence possible the most damning evidence But the criminals would be able to sneak out the back of the vase So let's eliminate let's look from the police's point of view again. What is better the SWAT team or detective Sandra for the police?
00:28:03
Speaker
Okay. Well, in that case, well, if you look at the SWAT team, they're going to have just proof, correct? Yeah. And she's going to have witnesses. So witnesses are worse than proof. Witnesses are worse than proof. So in that case, the best option would be the SWAT team. So now we know exactly what was going to happen.
00:28:21
Speaker
So now we've eliminated all of the worst choices and so, yay. So what we got is the last choice, which is that the SWAT team is best for the SWAT team to go into less knob. Exactly. It's better. It's the most logical option for both sides.
00:28:37
Speaker
And that is iterated elimination of strictly dominated strategies.
Game Theory in Various Contexts
00:28:41
Speaker
And I like this, but can you give me an example of where this is used? It's used in basically solving game theory matrices. I'm actually not sure. You mean it's just a logic puzzle? Well, it is a logic puzzle, but also, as we're going to talk about on our next episode, the final one about game theory.
00:28:59
Speaker
Stuff these are essential tools in building the understanding and techniques used in doing things like analyzing global warming for example because global warming is a
00:29:13
Speaker
Oh, because kind of like an if this then that, if this then that kind of thing. Well, it's a cooperative game where the pot is the atmosphere, but it's also a game where the players are not acting rationally. Like if you look at the evidence, if you look at... Well, some are going to act rationally, but some of them are acting... Well, in other words, there's value to their decisions. And by irrational, I don't mean in like a... I mean, there's incredible amount of evidence for the fact that we're doing massive amounts of ecological damage.
00:29:41
Speaker
But what I'm thinking is that basically that you're saying like some people will make decisions and the decisions are the worst choice and then some people make decisions and those decisions are the best choice, right? Yeah, and some people will make irrational decisions which are usually because of imperfect thought processes. So like countries do that when they don't act on climate change because they don't want to be the first one to have to enact policies that'll make them less money.
00:30:07
Speaker
Well, because there's lack of trust and there's no cooperation. Right. So this is basically used for analyzing complex situations. Yeah. The cold war, this was used a lot. Um, and they ignored all the evidence. I mean, all the, uh, answers. Yeah. And von Neumann, uh, but he is a development of, he developed game theory in various ways. At one point he thought that, um, small nuclear bombs are the most peaceful option because they deter people from using larger nuclear bombs. He later thought that was a bad idea.
00:30:37
Speaker
Oh, how interesting. Okay. So that's for, that's for the cold war. Yeah. So this is developed way back when. Yeah. It started in like the thirties or forties.
00:30:45
Speaker
Wow, okay. Okay. So so it actually is used in I mean, it could be used in obviously real-world situations as well Just not just playing around with you know, Johnny gets a haircut then It's important in business school to apparently there's some elements of game theory that are taught in business some business school so I would imagine kind of that was where I thought maybe it was gonna go to is to business decisions or I can you know economic things, but I wasn't sure I
00:31:15
Speaker
Yeah, definitely, it's a really interesting field. Game theory is all about decision-making, and strategies can help define games. Strategies are decisions based on the idea that other people can make their own decisions, and that those decisions can be weighed. On the next and final episode, we're going to talk about real-world applications and consequences of game theory. I am Sophia, and this has been Breaking Math. With us, we head on Diane Baca, my mom, and is there anything you want to plug?
00:31:59
Speaker
We are selling a poster on Patreon.
00:32:05
Speaker
for a recurring donation of $22.46 or you can buy it at our Facebook store on our Facebook page and $22.46 is pie to the E dollars. So that's kind of fun. Is that fun? It was fun. Thank you for letting me to be on this show. No it's pie to the E dollars fun. Oh yeah pie to the E dollars is so much fun.