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.