Our second idea model,
called the "El Farol" problem,
is a little more complicated than the Prisoner's Dilemma,
and was designed to illustrate ideas about self-organization and cooperation
in economics.
This model was constructed in order to display some of the flaws
in some of the assumptions made by traditional economics research.
Namely, that economic agents are
perfectly rational, self-interested individuals
who have complete knowledge of one another's strategies,
and can do perfect deductive reasoning.
Of course, economists don't believe this is true of agents,
but these assumptions actually make mathematics possible to do
on economic problems.
And the result is the notion of efficiency.
That is, that in some sense,
the agents working collectively, even though they are self-interested,
can lead to a situation that's the best possible situation for all.
This notion was first proposed by Adam Smith,
back in the 1700s,
and it has come to be called the "invisible hand".
Adam Smith, in 1776, in his book,
"An Inquiry into the Nature and Causes of the Wealth of Nations"
stated this famous quotation.
This is one of the first statements by an economist
that gets of the notion of emergence.
That is the notion that some invisible hand,
that is the collective action of selfish individuals,
gives rise to an unexpected phenomenon,
which is in this case, according to Adam Smith,
the annual revenue of society.
There's been a lot of controversy about these ideas
throughout the ages.
The part that we're going to address here is
those traditional economic assumptions of complete rationality
and the ability for deductive reasoning
that's assumed on the part of economic agents.
These assumptions have been questioned
particularly in a relatively new approach to economics
that's been called complexity economics.
That's come out of a number of meetings
starting at the Santa Fe Institute.
One of the first meetings there
involved collaborations between physicists and economists,
and led to a series of books called
"The Economy as an Evolving Complex System"
This is number one, and there's also number two and three,
and some other volumes, related to these efforts.
The idea of complexity economics
is that agents are self-interested,
but they have bounded rationality
which means that their reasoning
isn't necessarily always perfectly logical.
They have limited knowledge
of one another's strategies,
perhaps no knowledge at all,
and each agent does primarily
inductive, rather than deductive, reasoning.
Finally, very importantly,
agents adapt over time
to an ever changing environment.
In summary, the approach of traditional economics,
is to be able to make predictions,
using analytic or mathematical models,
assuming what's called
equilibrium dynamics,
where the environment
is relatively static.
Whereas complexity economics,
acknowledges that analytic models
are not always possible,
that equilibrium conditions are
never reached in the real world,
and often what's needed are
agent-based models
where the agents are able to adapt.
One of the founders of complexity economics
is an Irish mathematician and economist
name Brian Arthur,
who worked at the Santa Fe Institute
for many years,
and proposed the so-called
El Farol problem
which takes its name from
one of his favorite bars
called El Farol
on Canyon Road in Santa Fe.
This bar became the subject of a
very famous paper that Brian Arthur wrote,
called "Inductive Reasoning and Bounded Rationality"
I've put a link to that paper
on our course materials page.
And that spawned many other papers
and many research efforts
that used this idea model
including a paper by John Cassidy
that refers to the El Farol problem
as the most important problem
in complex systems theory.
I dont' know if that's true,
but it certainly had a great influence
on discussion about many of these issues.
So here's the problem.
El Farol had a very popular live Irish music night,
every Thursday night,
and in the formulation
told by Brian Arthur,
about 60 people fit comfortably inside,
where the music was,
but there were a hundred people
who wanted to go.
But those people want to fit comfortably
so they only wanted to go if
sixty or less are going to go.
However, there's a problem.
These people can't communicate with each other.
So that's part of the model
So we have these hundred independent people
who want to go,
but they only want to go if sixty or less
people are going to go.
And the only information that each person has,
is some historical data,
that is they know how many people attended
on each of the last say M Thursdays,
where everyone is using the same value of M,
and M stands for memory.
This is the memory that people have.
For example, if M is 3,
you might have the following information,
that three weeks ago, 35 people attended.
That was a pretty good night.
Two weeks ago, however,
76 people attended.
and it was awful, crowded in there,
not enjoyable for people
and then one week ago,
20 people attended.
Virtually empty.
So that's the kind of information
that each agent has
in this problem.
And each person, on every Thursday night,
has to independently make a decision.
Should I go?
So the question is
how is it that all these people
can cooperate, in a sense,
without communicating and
without any rational deductive reasoning.
This model of course
is a metaphor for many kinds of
cooperation problems that occur in economics
and other social sciences,
which is why it has been so influential.
There's many different versions of this,
but I'm going to talk about
the model that is in the
NetLogo models library.
I put a slightly modified version of it
on our course materials page
which I'll show you in a minute.
So let's talk about how the model works.
Here's how a person decides
whether or not to go.
In our model,
we have a hundred people.
Each person has some number of strategies.
We'll call it N.
And a strategy is a way of using information from past Thursdays
to predict the attendance this Thursday.
So each person has a possibly different set of strategies.
For example, let's suppose N=3.
Each person has 3 strategies,
and your strategies might be these.
First one might predict that
attendance will be the same as last week.
Strategy 2 might predict
that attendance will be
100 minus the attendance last week.
Strategy 3 might predict that attendance will be
.2 times the attendance of last week
plus .1 times the attendance two weeks ago.
And so on ...
You can make any number of strategies like this,
and some of them will be
very bad at predicting,
and possibly some of them will be good at predicting.
An important point though,
is that the environment might change,
and so the strategy that is best
at predicting might change also.
And so the agents have to be able to adapt.
Each time step of the model
corresponds to a new week,
a new Thursday,
on which you must decide
whether you're going to go or not.
And here's how you do that.
First you determine which one of your strategies
is the current best,
and that means the one that
did the best job of
predicting the actual attendance
that you saw on the previous Thursdays.
So once you do that,
you use your current best strategy
to predict the attendance for this Thursday.
If it predicts more than 60,
you don't go.
If predicts 60 or less,
you do go.
While you're doing this,
all other people in the model are also
doing the same thing,
simultaneously and independently,
with no communication.
OK, so this is a little bit of a
complicated model
so I'm going to have you take a short quiz
to make sure that you understand it,
and then we'll go over the answers to the quiz,
and then we'll go through some of the more detailed parts,
and the more detailed parts are going to be optional for you to watch.
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