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Path Dependence and Increasing Returns
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Del curso dictado por University of Michigan
Model Thinking
1135 calificaciones
De la lección
Path Dependence & Networks
In this set of lectures, we cover path dependence. We do so using some very simple urn models. The most famous of which is the Polya Process. These models are very simple but they enable us to unpack the logic of what makes a process path dependent. We also relate path dependence to increasing returns and to tipping points. The reading for this lecture is a paper that I wrote that is published in the Quarterly Journal of Political Science
Conoce a los instructores
Scott E. PageProfessor of Complex Systems, Political Science, and Economics
Center for the Study of Complex Systems
Hi. Remember we were talking about the concept of path dependence. In this
lecture, I wanna focus on a very closely related topic, or concept, known as
increasing returns. Increasing returns works as follows. Basically, it says, the
more I have of something, or the more people that do something, the more that I
want of it, or the more other people are gonna do it. So, for example, the more
people to get [inaudible] typewriters, and the more other people are gonna wanna get
[inaudible] typewriters. And there's two reasons for this. One is, you can then
type of somebody else's machine if they have the same layout. And then also, from
a production standpoint, if I'm producing [inaudible] typewriters. [inaudible]. Then
it makes more sense to these other [inaudible] that it's gonna be costly to
rearrange the keys on a computer. So there's these positive feedbacks. More
produces more. Now, this idea that more produces more actually. Exist within the
player process, right? The more blue balls I pick, then the more likely I am to get a
blue ball in the future. So, that leaves a lot of people to think, well maybe it's
increasing returns that causes path dependence. And in fact there are books
that are called Path Dependence Increasing Returns, and they're not necessarily
equating the two, they're just putting them in the same box saying that these are
related concepts. And they are related concepts because both the sway of the
paths process and the player process had increasing returns. And the balancing
process, which did not produce path dependence, didn't have increasing
returns. In fact, it had the opposite, it had decreasing returns. The more red balls
I picked, the more blue balls I picked in the urn. So there's clearly a relationship
between the two. What we'd like to do is understand, is it logically the same
thing? Is increasing returns the same thing as path dependence, or is it
something separate. Let's go back and look at our [inaudible] process. We've got one
blue ball and one red ball. We select a ball and then we return it, and we add a
ball of another color. This clearly has increasing returns. Because if I pick
three red balls. Now I've got four red balls in there, and only one blue. And the
odds of picking a red ball is gonna be four-fifths, whereas, initially, one-half.
So the more red balls I pick, the more likely I am to pick red balls in the
future. So there's clearly increasing returns in this setting. But what we wanna
ask is, does that mean that increasing returns is the same thing as path
dependence? Are the logically the same thing? Now here's where it's very useful
to have a model. And what we're gonna do is we're just gonna use our earn model,
and we're gonna see that, in effect, they're not the same thing. So here's
something I call the Gas/Electric Model and what this is meant to represent is the
choice between gas cars and electric cars. Now, both of these had positive feedback.
So when automobiles are first being developed, the more gas cars that were
going to be built, the cheaper it would be for other people to build gas cars because
all the engines would be being built, in fact, because there would be all these
subsidiary industries creating things like pistons and stuff like that and fuel
injectors. And so gas would be get more gas and also would create gas stations and
that sort of thing and a whole oil industry. And electric would also
[inaudible] electric so there would be electric filling stations and that sort of
stuff, so both had increasing returns. But the fact is, is that the turn of the
century when automobiles were being [inaudible] gas had much larger increasing
returns than did electric so here's how we can represent that. We're gonna start off
with five blue and blue is gonna represent gas. And we're gonna start out with one
red. Now let's suppose that somebody makes, a company rises up that's an
electric car company. Well what that's gonna do, is that's gonna add another red
car, another, another red ball in the air, because it's gonna make electric cars more
likely. But it's also gonna add one blue. Why? Because you can just stick a gas
engine on the electric car. And just like you could stick an electric engine on a,
on a gas, so we're assuming there's one blue and one red. Well what happens
initially I've got a one-fifth chance of getting a red ball, after I pick a red
ball I've got, since I've added one red and one blue. What I'm gonna guess, I'm
gonna have a two-sevenths chance. So the probability of picking a red ball has gone
up. But I would assume that increasing returns to, to blue balls, are much
larger. So if I pick a blue ball, then what I'm gonna add is ten blue balls.
Well, clearly if I pick a blue ball, then I'm increasing returns in blue balls. So
what I've got here, I've got increasing returns in red and increasing returns in
blue. But if you run this process, what you get is every single time, you're gonna
get the blue balls winning out. You're going to end up getting that blue balls
are more likely than red balls. And so this process isn't path dependent, but it
has increasing returns. It's just that the increasing returns are much larger for the
blue balls than they are for the red balls. So if you reregistry 1,000 times,
we'd get gas cars everytime. And the main reason is you couldn't carry electricity
in a tank. [inaudible] just carry electricity around. Take it, you know,
from one place to the next you couldn't store it and that storability meant that
gas cars had much more, had much larger increasing returns which is why they won
out. So, increasing returns themselves don't give path dependent. You can have
increasing returns and not get path dependent. Then we can ask another
question which is, could you. Get path-dependence without decreasing returns
and the answer to that is also yes. So here's an example and this [inaudible] an
example for symbiosis, so we've got a bunch of symbiots that get, now we've got
four color blocks. We've got blue, red, green and yellow and the [inaudible]
return it. But here's the idea, if I pick a red ball. I'm going to add a green. If I
pick a green ball, I'll add a red. If I pick a blue ball, I'll add a yellow, a
yellow ball, I'll add a blue. Well there's no increase in returns here. So if I pick
a red ball, I'm actually increasing the odds of green. But if pick a blue ball, I
increase the odds of yellow. The same goes for green and yellow, so there's no
increasing returns. I'm actually helping another type. But if I call this. The red
and green balls are star, for like the larger set of red balls. And I call this
blue star. You can see that this is in fact just the player process renamed. If I
pick a ball from this set, a red or green, I add another ball from that set. And if I
pick a ball from the blue yellow set and I add another ball to the blue yellow set.
So, this is going to be path dependent, but it doesn't have increasing returns.
So, what we see from the gas electric process is that. You can have increasing
returns, but not get path dependence. And what we see from symbiotic process is that
we can have path dependence and not have increasing returns. So, does this mean
that increasing returns doesn't matter? No, but it means that increasing returns
is logically distinct from path dependence. So, yes it may be the case
that a lot of the things that we out there in history in which we have path
dependence are the result of increasing returns, but. Logically they're completely
separate concepts, increasing returns can give path dependents but it doesn't have
to path dependents can occur with increasing returns it can occur without
it. And the earn models are really interesting, and they really help us
clarify a lot of stuff. But I don't want you to think that they're the only way you
can get path dependence. In fact, in my own opinion, I think most path dependence
comes from a very different process. And so I think we oughta just move beyond
earns, and talk about path dependence in the social realm occurring through
something entirely different. And that something entirely different is gonna be
externalities. It's gonna be interdependencies between decisions.
Remember and externality is a situation where I make some choice, A and this is
just me making this choice. So I choose A and I'm really happy, but when I choose
that, if you're over here, this has an effect on you. And maybe it makes you
happy or maybe it makes you sad, but my decision influences you. And these
externalities, because of the inter-dependencies between the choices,
can produce externalities that can do so in really obvious ways. So let me give
something that worked on, on my dissertation, my dissertation was written
on sort of externalities between large public projects. Now, why large public
projects? Because public projects are big. If you think of the economic choices we
make, me buying, me buying a loaf of bread is a little decision. Somebody building a
nuclear power plant, somebody, you know, creating a giant national park.
[inaudible], you know, creating [inaudible] interstate highway system.
These are huge economic decisions, and they bump into a whole bunch of other
stuff. And because they bump into a whole bunch of other stuff, they create extra
[inaudible]. And let's see, now, how those same externalities create path dependence.
So, here's my model. There's just gonna be five projects a, b, c, d, and e. Each one
has a value of ten on their own. This can be 10,000,000, 10,000,000,000, it doesn't
matter. There's a positive value of ten on their own. But, each project's also gonna
create some externalities. So, it's gonna. Bump into the other projects. And we'll
see how, now, we can get path dependence. So, here's how I'm gonna represent these
externalities graphically. The A, these things on the diagonal, the A, B, C, D, E,
it's just the value of the project. This minus twenty counts the size of the
externality between project A and project B. And this minus ten tell the size of the
externality between B and C, and this five. Gives the size of the externality
between A and C. So let me, get rid of all of my drawings here, and now let's think
about, supposed that I did project A first. I get a value of ten. Now I'm
thinking, do I do B? If I do A and B, I'm gonna get ten for A, plus ten for B, but
then minus twenty for A and B which is gonna be worth zero, so I'm not gonna do
it. Now if I think about doing A and C. I'm gonna get ten for A, plus ten for C,
but then I get plus five for AC, which is gonna be 25, which is bigger than this
ten. So I'm gonna do AC. Well now I've gotta ask, do I do A, C, and D? And if I
do A C and D, I'm gonna get ten for A. Plus ten for C, plus five for the
externality, plus ten for D, but then minus ten. For the externality between A
and D, and that's gonna mean that, you know, maybe I do it and maybe I don't,
because I'm sort of indifferent between doing A and D. So you can see if I start
with A, I'm not gonna do B, I'm gonna do C. Maybe I do D, maybe I don't. Well,
let's suppose that for some reason, I start out by doing B first, and if I do B
first, then I'm gonna get a path of ten, and for the reasons I didn't talk about
before, A B is getting a dim value of zero, so I'm not gonna do A B. But now
when I look at B and C. If I do B and C, I get ten for B, ten for C, but then the
externality between B and C is -ten. And so I'm not going to get really any larger
benefit from doing B and C, so I could decide to do it, I could decide to not do
it. Let's suppose I decide not to do it. When I also get B and D, and I look at B
and D, I get ten for B and ten for D. But the externality between B and D is 30.
Which is positive right? So now that's [inaudible] 50, so I'm gonna do B and D.
So what's interesting here is if I started out, doing A I might end up A and C. If I
start out doing B I might do B and D. And so there's gonna be depending on not only
the initial conditions but also sort of you can see as I moved down this path,
what projects I do in the past, are going to effect. What projects I do in the
future. So these externalities between projects create path dependencies along
the way. And it's the positive externalities as well as the negative
externalities between projects. And what I did in my dissertation was showing that if
most of the externalities were positive, then you actually had less path dependence
than if the externalities were negative because the positive externalities
created, they gave me sort of increasing returns of public projects, and just made
it more likely that you're gonna do more projects. And you didn't get as much
contingency as when you had the negative externalities. The point I want you to
take away from this is, a big cause of path. [inaudible] is externalities and
increasing returns I guess to one type of externality between decisions. Okay, so
let's think about this particular lecture. What have we done? We said that one thing
that people often equate with path dependence is increasing returns and we've
shown that although maybe empirically the case that a lot of path dependence does
come from increasing returns, logically they're completely separate. You can have
path dependence without increasing returns, you can have increasing returns
and not get path dependence. We also talked about how one big cause of path
dependence may be externalities. Inner dependencies between choices, especially
big choices like public projects, and those externalities, whether they're
positive or negative. Can create that dependence. But the negative [inaudible]
may have a larger effect. All right, thank you.
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