What do you think of

when you hear the phrase "game"?

maybe you think of your favorite childhood
board game

or maybe you think of an athletic 
competition

maybe you think of the games people play

in their everyday social interactions

all of these, as well as countless other
scenarios

are accurate notions of a game

but what ties them together?

The answer is that all games involve more

than one decision maker

Game Theory is a tool for analyzing such

scenarios, and the fundamental subject
of this tutorial

To really understand the difference
between a game,

and the individual agent's decision 
problem,

let's look at an example

Assume you live alone

and are deciding what to cook for dinner

You go home, you open your refrigerator,

you see you have some chicken, some
spices,

and you decide to make an Italian chicken

Now, this is great, because you are

coordinating the entire dinner, you make
some nice sides,

and your dinner is very tasty
because I know you are a good cook

Now, imagine a scenario where you are

cooking with your friend,

and you want to make the same Italian 
chicken,

but what if your friend is making 
Chinese side dishes?

I have to tell you, that would not
be a dinner that I'd want to eat

not very harmonious

What you have to do is you have to
coordinate with your friend

You have to let your friend know that you
are making Italian chicken,

so that they make an Italian side dish

This is known as a coordination game,

and in fact, is a canonical example

of a game that you would learn in 
an introductory Game Theory course

Even in this simple example,

the second case, in which you have to 
coordinate,

is much more complicated than the first

In the first case, you only care about

cooking the tastiest meal, and you don't

really think about how the chicken is
going to react to you

In the second scenario, however, you care

about not just what you make, but how your

dish works with your friend's dish

The crucial element is that the same time,

your friend is also going through a

similar decision making process

This is sometimes known as a multi-agent

optimization problem, and forms the

essence of what is called a strategic

scenario, and we use Game Theory to

analyze strategic scenarios

For those of you familiar with decision
theory,

one similarity between Game Theory

and Single Agent Decision Problems

is that we assume agents are rational,

utility maximizers

By utility maximizers, we just mean that

agents choose the action that is best for
them

By rational, we mean that they don't make

mistakes in choosing that action

Now, if this sounds funny to you, or

unreasonable, that's okay,

the second tutorial in this series will

cover Behavioral Game Theory which

is what happens when we relax these
assumptions

If you are coming to this tutorial, you

are probably interested in Complexity
Science,

and are wondering, why does a Complexity 
Scientist

need to know Game Theory?

The long and short of it, is that

Game Theory can be used as a building

block for larger complex models

For example, one complex system that we

are interested in is cities

We might be interested in the migration

patterns; we might be interested in the

business patterns; we might be interested

in the scaling of cities; and in fact,

one other element of cities we might be

interested in is the traffic flows

But if you think about it, traffic is the

outcome of a game

Why? Well, it is people, or maybe even

robots, making decisions about where and

when to drive

In a famous example, known as

Braess's Paradox, we can use Game Theory

to show that adding a road to a traffic

network can actually increase the amount

of delays

This is just one of the many examples of

how Game Theory can provide insight into

a complex system

Other examples include air traffic control

systems, national security, environmental

regulation, stock markets, and computer

networks

Unfortunately, we won't be able to cover

all of these in this tutorial, but we will

certainly touch on a few

Given the wide range of Game Theory

applications, what will we be covering

in this course, and what is our goal?

We will begin by introducing main

definitions in standard Game Theory

courses

These include strategies, payoffs,

utilities, and of course, equilibrium,

and after laying this foundation, we will

work through several examples that will

illustrate key phenomenon that appear in a

wide variety of games

All but one of these lessons only requires

basic Algebra, while one optional lesson

requires calculus

In general, the goal of this course is to

build a foundational understanding of

Game Theory, so that those interested in

incorporating Game Theoretic aspects into

the Complex Systems model will feel

comfortable doing so

If you get stuck, remember there are

quizzes to help guide you along the way,

and I really hope you enjoy these videos