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