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Hi. In this lecture, we're gonna compare and contrast the three ways we've thought

Â about modeling people. So remember we talked about first people being rational,

Â people having objective functions, and optimizing with respect to their

Â objectives. Then we talked about how that's somewhat unrealistic. We talked

Â about the behavior models, and I tend to think of these as rationality plus, where

Â we sort of assume rational behavior but then we add in a bias, or rationality

Â minus, is sort of being a little bit below rational behavior. And then the third

Â thing we did is we said well you know, maybe we could even go simpler and we

Â could just assume that people follow rules. These could be fixed rules. They

Â could be adaptive rules. And when you write down a model, you could say here's

Â the rule that people follow. Now in some cases, the rule that people follow will be

Â rational. In some cases, the rule that people follow will be behavioral. In other

Â cases, the rule that people follow will just be some rule that we made up. What

Â I'm going to do in this lecture is I'm gonna ask does it matter. Does it matter

Â which rules we write down? Does it matter whether you have rule based behavior,

Â optimizing behavior, or behavioral models? Well, the answer is it depends. And one of

Â the reason why we model is to figure out how much does it matter how effectively we

Â model, or how accurately we model I should say. So, let me do two examples. First,

Â I'm going to talk about a market, just a pure exchange market. And then I'm going

Â to talk about a game, called Race to the Bottom. You're gonna see in the market, it

Â really doesn't matter that much how we model behavior, but in the Race to the

Â Bottom. You're going to see, it matters a lot. So let's get started. So a two-sided

Â market. What is a two-sided market? Well, a two-sided market has a group of buyers;

Â and these are people who want to buy some good. And let's suppose. Just for the sake

Â or argument, that these buyers in the setting have prices between zero and $100,

Â that means they're willing to pay somewhere between zero and $100 for this

Â good. Now in addition to the buyers, there are some sellers and let's suppose the

Â sellers are wiling to sell. For between 50, and 150 miles. So now let's think

Â about, what would rationale people do. So those people who are complete rationale,

Â in this setting. How would they behave? Well. If you're a buyer. You basically be

Â it a little bit less. Right then your true value because you'd try and make a little

Â bit of money. And if you're a seller, you'd probably ask for a little bit more

Â than your true value. And how much more or less you ask for is gonna depend on, you

Â know, what the distributions of these buyers and sellers are. So if you're fully

Â informed about what other people, what these distributions are, you're gonna

Â shade in particular ways. Now what's gonna happen is, let's suppose that people keep

Â on calling out prices until the market clears. Until the number of goods sold,

Â that people want to sell at that price is exactly equal to the number of goods

Â bought. The way it's going to work is each person calls out each buyer calls out a

Â price their willing to buy at, each seller calls out, a price they are willing to

Â sell at, and then we pick some sort of price in the middle so we get an even

Â number of buyers and sellers. But what's going to happen in the situation is that

Â the only buyers, that are gonna have a value of at least 50 since people are

Â rational, the only buyers that are actually gonna be, be able to buy anything

Â are going to have a value of about 50. So the relevant buyers. Are gonna have values

Â in 50 to 100. So we only need to worry about these people. So we can call these B

Â star. And the relevant sellers are gonna be the only ones that advise between 50

Â and 100 as well. Because the ones that have values above 100, from 100 to 150,

Â they want too much. Nobody, nobody's willing to pay that much for their goods.

Â [inaudible], people are gonna call out these prices, and what we're probably

Â gonna get is we're probably gonna get a price of around 75, right? Where some of

Â the buyers buy, some of sellers sell, but not all of them do. Let's suppose instead

Â we assume people are biased, that they're not super strategic in figuring out

Â exactly how much to shave their bids. Well then what people would probably do is they

Â might rely on sort of focal bids. So people would be more likely to bid like

Â 50, or 60 or 70 or 75. Even increments. So, let me be more specific. So it might

Â be that if your rational buyer your value is 56 that what you should do is you

Â should say I'm willing to pay 53.72 cents Right you solve some really fancy

Â mathematical equation. [inaudible] That's exactly your optimal bid. Well a

Â behavioral person might not do all that. Ask. And it might say well my value's 56

Â so I'll bid 52 or I'll bid 50, 55, right. Just some focal number. They're not going

Â to do all the math. Well again, if there's just those slight deviations, you're still

Â probably going to see a price of about $75. So optimizing behavior and sort of

Â slight behavioral bias is not going to be a big difference. What about rule based

Â behavior? Well this has actually been studied using a simple rule base called

Â zero intelligence agents. This is ZI, we'll abbreviate it. So zero intelligence

Â agents work as follows. If you're a bidder, what you do is you just sort of,

Â if you're a buyer, what you do is just basically say okay, I'm just going to pick

Â some random amount less than my value. And if you're a seller, you just pick some

Â random amount more than your value. So if you're a buyer, and your value's 40.

Â Right, so if I'm the buyer who's value's 40, I might say, oh, I'm willing to buy it

Â for twenty. And if I'm a seller who's value's 60, I might say, oh I'm willing to

Â sell it for 63. So what happens is, is you just choose some random amount. What turns

Â out if you analyze the [inaudible] market with. >> These zero intelligent traders.

Â What you end up getting is something with a price pretty close to 75 and not that

Â different from what you'd get with rational actors. So, in a two sided

Â market, right, [inaudible] and things, you know, we've got models in economics, we've

Â got sort of supply and demand curves and things like that where we get some price.

Â It turns out the market itself has so much influence. The institutions have so much

Â influence. The behavior really doesn't matter a great deal within some fairly

Â wide range of [inaudible]. So in markets, we don't care as much about [inaudible]

Â behavior. But now in games, we do. So let's do a specific game, it's called the

Â race to the bottom game, and here's how it works. You pick a number between zero and

Â a hundred, the whole group, the group of people in the room. Each person's gonna

Â pick a number between zero and a hundred, whoever's closest to two thirds of the

Â mean. Wins. Alright, so what do you do? Little quiz, what do you do in this

Â situation? Well. Let's, let's look. So what does a rational person do. So if a

Â rational person is gonna be in this situation it turns out is bid zero. Why is

Â that. Well, it's a completely symmetric game. Everybody's got the exact same

Â sentence, everybody is rational, everybody should be doing the same thing. So suppose

Â everybody was picking six. If everybody was picking six, then the mean would be

Â six. If the mean is six, two-thirds of six is four, so if you're rational and you

Â know everybody's picking six you should pick two-thirds of six so you should pick

Â four. So, but then if everybody, then everybody should pick four. But if

Â everybody's picking four, then you should guess two-thirds of four, right? Which is

Â 8/3. [inaudible] of everybody else. If everybody's picking 8/3 then you should

Â give two-thirds of 8/3, and so on, and so forth, and so on. Until eventually you get

Â down to everybody should be bidding, 0's. That's what rational [inaudible] would be.

Â What would bias behavior be? Well, if you were sort of. Not strategic at all. I'm,

Â super biased in this situation. Say, okay. Fifteen and a number between zero and 100.

Â I don't know [inaudible] thing. I'm confused. What I'm going to do is I'm

Â going to guess 50. And in fact if you watch people play this game there's a

Â certain percentage of people who do guess 50. And in fact, you know, I've done this

Â in my classroom a whole bunch of times and you'll get a significant percentage of

Â people who just say I'm going to guess 50. Now, what would a behavioral rule be in

Â this situation? What would a rule based behavior be? Well, again this is the

Â instance studied a lot and a rule that people tend to study is this. They say

Â well, you know, people should guess 50. If everybody guesses 50, I should guess

Â two-thirds of 50, so therefore I should guess 33. So you see a lot of people guess

Â 33. But then there's a lot of other people who say "you know what everybody should

Â guess, is going to guess, so if everyone's going to guess 33, I should guess

Â two-thirds of 33". Which is 22 and so if you look at. With the experiment, you see

Â sum 50, sum 33, sum 22's in some. Right two thirds of 22 is fourteen so you see,

Â some people actually say this. Look, people should guess 50 [laugh], so some

Â [inaudible] should guess 50, I guess two thirds of 50 which is 33. [inaudible]

Â Everybody should guess 33. So then I guess two thirds of 33 which is 22. If anybody's

Â gonna guess 22. So I guess two thirds of 22 which is fourteen. Now of course if we

Â kept going with this we get to the rational behavior eventually, which is

Â zero. Right? And, in fact if you played this long enough these number do creep

Â down to zero, but they don't, typically don't get there. You have to run them a

Â lot of times. So it's interesting here is, the behavior we see is, this rule is sort

Â of a mix of rationale. And the buyer. So the buyer's thing is to get 50. So people

Â sort of start with the base three by 50 stays in the middle. After that they start

Â sort of test responding. Never on an adaptive rule for learning what?s the best

Â response. So the best responsibility, best responsibility ?cause its 50 is to choose

Â 33. And the best response ?cause choosing 33 is to choose 22 and so on. So here's

Â what we see, is the rules that people use to sort of start up with the [inaudible]

Â buyers Someone rational. Let's do something really fun here. [laugh] So

Â let's suppose we have two rational people in this game and one irrational person. So

Â let's suppose you're sitting in a [inaudible] space with three people and

Â you're a rational person, let's say you've seen this game before, you know how it

Â works. And you're playing with me and you know I've seen this game before and I know

Â how it works. But there's this third person sitting in the room and this third

Â person we don't know anything about. We know that they haven't seen the game

Â before and they, you know. Here are the instructions. And we're both looking at

Â him trying to figure, what is this person going to do? Well. Let's try and analyze

Â this. So suppose I'm a rational person, and you're a rational person. So we're

Â gonna pick sum amount R, right? Now, the other person, the [inaudible] person,

Â you've gotta make some decision, like, what do you we think they're gonna pick?

Â Well, suppose we both think they're gonna pick X. Well, if they're gonna pick x, we

Â have to decide how much do we pick, what do we pick. Well, here's what has to be

Â true. The amount we pick r has to be two thirds of r plus r plus x, right? Because

Â it's gotta be two thirds of the sum of everybody else's, divided by three. So

Â it's gotta be two thirds of the mean, so it's gotta be two thirds of r plus r plus

Â x, divided by three. So if I multiply this out, I'm gonna get nine r. Has got to

Â equal 2xR+R+X, right. And so I'm going to get, this ends up being 4R so I'm going to

Â get 5R=2X. So R equals. 2x over five. So what that means is we both think "oh, this

Â other person is". What, I don't know. Totally irrational, supposed to think the

Â other person is gonna choose 50. We think the other person is gonna choose 50. Then

Â r equals two times 50 over five, r is gonna equal twenty. Right, so if the other

Â person chooses 50. And we both choose twenty, the sum will be 90. Right, so the

Â average is 30. And so two thirds of the mean will be twenty. So why did I give

Â this example. Just think back. If everybody is rational, the mean is zero.

Â The mean bid is zero and two-thirds of the mean is zero and we split the money. But

Â here we throw in one irrational person, then we no longer get zero. Right? We get

Â something a lot bigger than zero, because the rational people have to take into

Â account what the other person's bid is gonna be, and so they want to make their

Â bid as a function of that, and that drives up their bid which drives up the mean,

Â which in term drives up their bid. So, what's the lesson we take away? I think

Â the simple lesson is this, that rational behavior is a really good benchmark. But

Â it's also important to included biases in our model. Think about, are there biases

Â that would be relevant. And it's also important to think about what if we just

Â write down a simple rule. And then if we compare these three things. Rationale

Â behavior, bias. Right, and then simple rule. And we see, well, how much

Â difference do we see in the outcome. If the difference is small, then we can say

Â you can look our results seem to be sort of [inaudible] to behavior. If the

Â difference is big, then what you gotta do is you gotta sit back and think. Okay

Â which of these three makes the most sense. And regardless of [inaudible] modeling,

Â whether it's the, just the [inaudible] of the world. Whether it's [inaudible] to

Â understand data. Right, [inaudible] the logic right, or whether it's to. Design

Â something. Strategize in some way. It's probably really useful, to think about all

Â three classes of [inaudible], in the context that you're considering. Thank

Â