Hi. In this lecture, we're gonna compare and contrast the three ways we've thought about modeling people. So remember we talked about first people being rational, people having objective functions, and optimizing with respect to their objectives. Then we talked about how that's somewhat unrealistic. We talked about the behavior models, and I tend to think of these as rationality plus, where we sort of assume rational behavior but then we add in a bias, or rationality minus, is sort of being a little bit below rational behavior. And then the third thing we did is we said well you know, maybe we could even go simpler and we could just assume that people follow rules. These could be fixed rules. They could be adaptive rules. And when you write down a model, you could say here's the rule that people follow. Now in some cases, the rule that people follow will be rational. In some cases, the rule that people follow will be behavioral. In other cases, the rule that people follow will just be some rule that we made up. What I'm going to do in this lecture is I'm gonna ask does it matter. Does it matter which rules we write down? Does it matter whether you have rule based behavior, optimizing behavior, or behavioral models? Well, the answer is it depends. And one of the reason why we model is to figure out how much does it matter how effectively we model, or how accurately we model I should say. So, let me do two examples. First, I'm going to talk about a market, just a pure exchange market. And then I'm going to talk about a game, called Race to the Bottom. You're gonna see in the market, it really doesn't matter that much how we model behavior, but in the Race to the Bottom. You're going to see, it matters a lot. So let's get started. So a two-sided market. What is a two-sided market? Well, a two-sided market has a group of buyers; and these are people who want to buy some good. And let's suppose. Just for the sake or argument, that these buyers in the setting have prices between zero and $100, that means they're willing to pay somewhere between zero and $100 for this good. Now in addition to the buyers, there are some sellers and let's suppose the sellers are wiling to sell. For between 50, and 150 miles. So now let's think about, what would rationale people do. So those people who are complete rationale, in this setting. How would they behave? Well. If you're a buyer. You basically be it a little bit less. Right then your true value because you'd try and make a little bit of money. And if you're a seller, you'd probably ask for a little bit more than your true value. And how much more or less you ask for is gonna depend on, you know, what the distributions of these buyers and sellers are. So if you're fully informed about what other people, what these distributions are, you're gonna shade in particular ways. Now what's gonna happen is, let's suppose that people keep on calling out prices until the market clears. Until the number of goods sold, that people want to sell at that price is exactly equal to the number of goods bought. The way it's going to work is each person calls out each buyer calls out a price their willing to buy at, each seller calls out, a price they are willing to sell at, and then we pick some sort of price in the middle so we get an even number of buyers and sellers. But what's going to happen in the situation is that the only buyers, that are gonna have a value of at least 50 since people are rational, the only buyers that are actually gonna be, be able to buy anything are going to have a value of about 50. So the relevant buyers. Are gonna have values in 50 to 100. So we only need to worry about these people. So we can call these B star. And the relevant sellers are gonna be the only ones that advise between 50 and 100 as well. Because the ones that have values above 100, from 100 to 150, they want too much. Nobody, nobody's willing to pay that much for their goods. [inaudible], people are gonna call out these prices, and what we're probably gonna get is we're probably gonna get a price of around 75, right? Where some of the buyers buy, some of sellers sell, but not all of them do. Let's suppose instead we assume people are biased, that they're not super strategic in figuring out exactly how much to shave their bids. Well then what people would probably do is they might rely on sort of focal bids. So people would be more likely to bid like 50, or 60 or 70 or 75. Even increments. So, let me be more specific. So it might be that if your rational buyer your value is 56 that what you should do is you should say I'm willing to pay 53.72 cents Right you solve some really fancy mathematical equation. [inaudible] That's exactly your optimal bid. Well a behavioral person might not do all that. Ask. And it might say well my value's 56 so I'll bid 52 or I'll bid 50, 55, right. Just some focal number. They're not going to do all the math. Well again, if there's just those slight deviations, you're still probably going to see a price of about $75. So optimizing behavior and sort of slight behavioral bias is not going to be a big difference. What about rule based behavior? Well this has actually been studied using a simple rule base called zero intelligence agents. This is ZI, we'll abbreviate it. So zero intelligence agents work as follows. If you're a bidder, what you do is you just sort of, if you're a buyer, what you do is just basically say okay, I'm just going to pick some random amount less than my value. And if you're a seller, you just pick some random amount more than your value. So if you're a buyer, and your value's 40. Right, so if I'm the buyer who's value's 40, I might say, oh, I'm willing to buy it for twenty. And if I'm a seller who's value's 60, I might say, oh I'm willing to sell it for 63. So what happens is, is you just choose some random amount. What turns out if you analyze the [inaudible] market with. >> These zero intelligent traders. What you end up getting is something with a price pretty close to 75 and not that different from what you'd get with rational actors. So, in a two sided market, right, [inaudible] and things, you know, we've got models in economics, we've got sort of supply and demand curves and things like that where we get some price. It turns out the market itself has so much influence. The institutions have so much influence. The behavior really doesn't matter a great deal within some fairly wide range of [inaudible]. So in markets, we don't care as much about [inaudible] behavior. But now in games, we do. So let's do a specific game, it's called the race to the bottom game, and here's how it works. You pick a number between zero and a hundred, the whole group, the group of people in the room. Each person's gonna pick a number between zero and a hundred, whoever's closest to two thirds of the mean. Wins. Alright, so what do you do? Little quiz, what do you do in this situation? Well. Let's, let's look. So what does a rational person do. So if a rational person is gonna be in this situation it turns out is bid zero. Why is that. Well, it's a completely symmetric game. Everybody's got the exact same sentence, everybody is rational, everybody should be doing the same thing. So suppose everybody was picking six. If everybody was picking six, then the mean would be six. If the mean is six, two-thirds of six is four, so if you're rational and you know everybody's picking six you should pick two-thirds of six so you should pick four. So, but then if everybody, then everybody should pick four. But if everybody's picking four, then you should guess two-thirds of four, right? Which is 8/3. [inaudible] of everybody else. If everybody's picking 8/3 then you should give two-thirds of 8/3, and so on, and so forth, and so on. Until eventually you get down to everybody should be bidding, 0's. That's what rational [inaudible] would be. What would bias behavior be? Well, if you were sort of. Not strategic at all. I'm, super biased in this situation. Say, okay. Fifteen and a number between zero and 100. I don't know [inaudible] thing. I'm confused. What I'm going to do is I'm going to guess 50. And in fact if you watch people play this game there's a certain percentage of people who do guess 50. And in fact, you know, I've done this in my classroom a whole bunch of times and you'll get a significant percentage of people who just say I'm going to guess 50. Now, what would a behavioral rule be in this situation? What would a rule based behavior be? Well, again this is the instance studied a lot and a rule that people tend to study is this. They say well, you know, people should guess 50. If everybody guesses 50, I should guess two-thirds of 50, so therefore I should guess 33. So you see a lot of people guess 33. But then there's a lot of other people who say "you know what everybody should guess, is going to guess, so if everyone's going to guess 33, I should guess two-thirds of 33". Which is 22 and so if you look at. With the experiment, you see sum 50, sum 33, sum 22's in some. Right two thirds of 22 is fourteen so you see, some people actually say this. Look, people should guess 50 [laugh], so some [inaudible] should guess 50, I guess two thirds of 50 which is 33. [inaudible] Everybody should guess 33. So then I guess two thirds of 33 which is 22. If anybody's gonna guess 22. So I guess two thirds of 22 which is fourteen. Now of course if we kept going with this we get to the rational behavior eventually, which is zero. Right? And, in fact if you played this long enough these number do creep down to zero, but they don't, typically don't get there. You have to run them a lot of times. So it's interesting here is, the behavior we see is, this rule is sort of a mix of rationale. And the buyer. So the buyer's thing is to get 50. So people sort of start with the base three by 50 stays in the middle. After that they start sort of test responding. Never on an adaptive rule for learning what?s the best response. So the best responsibility, best responsibility ?cause its 50 is to choose 33. And the best response ?cause choosing 33 is to choose 22 and so on. So here's what we see, is the rules that people use to sort of start up with the [inaudible] buyers Someone rational. Let's do something really fun here. [laugh] So let's suppose we have two rational people in this game and one irrational person. So let's suppose you're sitting in a [inaudible] space with three people and you're a rational person, let's say you've seen this game before, you know how it works. And you're playing with me and you know I've seen this game before and I know how it works. But there's this third person sitting in the room and this third person we don't know anything about. We know that they haven't seen the game before and they, you know. Here are the instructions. And we're both looking at him trying to figure, what is this person going to do? Well. Let's try and analyze this. So suppose I'm a rational person, and you're a rational person. So we're gonna pick sum amount R, right? Now, the other person, the [inaudible] person, you've gotta make some decision, like, what do you we think they're gonna pick? Well, suppose we both think they're gonna pick X. Well, if they're gonna pick x, we have to decide how much do we pick, what do we pick. Well, here's what has to be true. The amount we pick r has to be two thirds of r plus r plus x, right? Because it's gotta be two thirds of the sum of everybody else's, divided by three. So it's gotta be two thirds of the mean, so it's gotta be two thirds of r plus r plus x, divided by three. So if I multiply this out, I'm gonna get nine r. Has got to equal 2xR+R+X, right. And so I'm going to get, this ends up being 4R so I'm going to get 5R=2X. So R equals. 2x over five. So what that means is we both think "oh, this other person is". What, I don't know. Totally irrational, supposed to think the other person is gonna choose 50. We think the other person is gonna choose 50. Then r equals two times 50 over five, r is gonna equal twenty. Right, so if the other person chooses 50. And we both choose twenty, the sum will be 90. Right, so the average is 30. And so two thirds of the mean will be twenty. So why did I give this example. Just think back. If everybody is rational, the mean is zero. The mean bid is zero and two-thirds of the mean is zero and we split the money. But here we throw in one irrational person, then we no longer get zero. Right? We get something a lot bigger than zero, because the rational people have to take into account what the other person's bid is gonna be, and so they want to make their bid as a function of that, and that drives up their bid which drives up the mean, which in term drives up their bid. So, what's the lesson we take away? I think the simple lesson is this, that rational behavior is a really good benchmark. But it's also important to included biases in our model. Think about, are there biases that would be relevant. And it's also important to think about what if we just write down a simple rule. And then if we compare these three things. Rationale behavior, bias. Right, and then simple rule. And we see, well, how much difference do we see in the outcome. If the difference is small, then we can say you can look our results seem to be sort of [inaudible] to behavior. If the difference is big, then what you gotta do is you gotta sit back and think. Okay which of these three makes the most sense. And regardless of [inaudible] modeling, whether it's the, just the [inaudible] of the world. Whether it's [inaudible] to understand data. Right, [inaudible] the logic right, or whether it's to. Design something. Strategize in some way. It's probably really useful, to think about all three classes of [inaudible], in the context that you're considering. Thank