Recently, I completed Professor Scott P. Stevens’s
24-lecture course for The Great Courses © entitled Games People Play: Game Theory in Life, Business, and Beyond – Parts I
& II. Though Professor Stevens is a Mathematician working at James Madison
University, this course
is taught under the Economics and Politics sections as these are the most
frequent applications of game theory. Each of the 24 lectures is thirty minutes
long for a total course time of 12 lecture hours. Professor Stevens presents
this introduction to game theory as a survey course and often avoids complex
mathematics (other than a few instances of basic calculus concepts) that is
essential to the actual application of game theory to the problems discussed in
the course.
Game theory has been a subject that crossed over into public
fascination with the release of the Russell Crowe biopic film about
Mathematician John Nash, a significant foundational game theorist. While Nash’s
concepts were poorly described by the film’s writers, the significance of his
contributions to the field was not. The beginnings of game theory start with
another famous mathematician name John, this one the exceptional genius and
polymath named von Neumann. He and an economist colleague, Oskar Morgenstern,
wrote the modern masterpiece on the subject of games: Theory of Games and Economic Behavior published in 1944.
Professor Stevens defines game theory as “the study of
strategic, interactive decision making among rational individuals.” “Any time,”
he asserts, “people make decisions that affect others or in response to the
actions—or even expected actions—of others, they’re playing a game.” Thus,
ideas in game theory apply equally well to such mundane decisions as where to
eat lunch as well as “earthshaking” decisions about the risk of nuclear war.
Fundamentally, there are three components to any game: players, strategies, and
payoffs. Throughout the first lecture, we learn that the concept of games
applies to almost any facet of life. Professor Stevens presents various
circumstances under which game theory can be applied in fields as diverse as
the military, politics, biology, NASCAR, and business strategy.
To better understand games, the instructor presents a simple
game. You are given $100 and a button that you can push. Another one hundred
people are given the same and each of you is unknown to the other. If you or
any of your competitors push your button every other player loses $2; if you
lose money because others push their button, pushing your button will cut your
losses in half. While it is rational for no one to press their button and take
home the $100, studies show that most people will press the button. Another
example of seemingly irrational behavior was demonstrated by Max Bazerman at Harvard Business School
who taught Wall Street Investors to think ahead by auctioning off a $100 bill.
The winning bid was $465.
Another classic example that applies to game theory is the
Federal auction for licensing of the radio spectrum. Historically, the US tried many
approaches to the sale of the radio spectrum that failed, in some cases
miserably. Game theorists stepped in and created a multi-objective auction
structure that successfully raised over $400 billion for the US Treasury in its
first 5 years. This is one example of many, in which the application of game
theory has shown to be advantageous in analyzing and approaching strategic
decisions.
The basics of game theory are fairly simple to explain.
Every game has three basic components: players, strategies, and payoffs. A
player is a decision maker in the game. A strategy is a specification of a
decision for each possible situation in which a player may find him or herself.
A payoff is the reward or loss a player experiences when they follow their
respective strategies.
Another distinction regards the type of game. For example,
when all players may “move” simultaneously without knowing what the other
player will do. Consider the simple childhood game, “Rock, Paper,
Scissors”—this is a rather crude example of a simultaneous game. Sequential
games are another variety. In a sequential game, one player moves first, giving
other players some knowledge about their choice. A simple example of a
sequential game is the familiar board game chess. A familiar term to many in
the public is the “Zero Sum Game” which is also a type of game in game theory,
although it is a bit different conceptually than what the common understanding
might indicate. Zero sum games occur when all of the losses and all of the
gains of all players are added up and equal zero. This is often evident before
the game begins.
Other classes of games include: Constant Sum Games, Symmetric
games, Perfect information games, Repeated games, Signaling games, Cheap talk
games, Mechanism design, Bargaining problem games, Stochastic games, Large
Poisson games, Nontransitive games, and Global games. Professor Stevens
introduces many of these concepts (though not all of those listed) but only
some are explored in-depth. To give my readers complete non-disclosure, these
games can often be very complicated to understand but the instructor is very
good at guiding one through the lecture. However, to truly understand these
concepts, repeated listening and perhaps further reading might be
necessary—they certainly would be for me!
The course expands upon these basics to examine more complex
aspects of games such as strategies, threats, promises, brinkmanship,
incomplete information, and chance. This array of factors in decision making,
as presented in game theory, has applications in fields as diverse as climate
change, voting, market entry, price setting, cooperative behavior and many more
things that are beyond the scope of this review.
Without delving too deep into the topic, it might shed a
little more light on the nature of the game theorist’s work by examining a few
of the aforementioned complicating factors that inhabit even simple games. For
example, strategies come in two varieties: pure and mixed. Pure strategies specify
an action for every possible situation in the game. There is no random
component to a pure strategy. Mixed strategies, however, does include some
randomness as a probability is assigned to each pure strategy—and since
probabilities are continuous there are an infinite number of mixed strategies
available to the player. A variant of the mixed strategy is called the totally
mixed strategy in which only positive values are assigned to every possible
pure strategy.
The next concept we will examine is that of the threat. Professor
Stevens explains that, in game theory, a threat is the equivalent of saying “Do
what I want or I will make things worse for you than you would otherwise
expect.” Promises, on the other hand, are the equivalent of saying, “If you
make this choice, I will respond with a choice that you’ll like—something that
you wouldn’t normally expect me to do.” Promises and threats are therefore,
conditional.
Games of incomplete information are those in which not all
of the players know the structure of the game—players might be uncertain about
possible strategies or payoffs of other players. These require complex analysis
and can have catastrophic consequences for some players. Finally, brinksmanship
might best be illustrated by thinking about the Cold War—because this strategic
element means to push dangerous events, such as the proliferation of nuclear
arms, all the way to the “brink of disaster” (think about the Cuban Missile
Crisis) in an attempt to achieve the most positive outcome in the game.
There are numerous topics in even a survey of game theory. A
simple summary of such a survey is necessarily incomplete. However, I feel that
I would be remiss if I did not include one of the most famous elements of game
theory in my little muddled examination: the Nash Equilibrium. Professor
Stevens explains that the way the movie A
Beautiful Mind, starring Russell Crowe, explains the Nash Equilibrium is
actually incorrect. The movie has Nash explain his equilibrium in terms of a
dating conundrum among a bunch of competitive men. The solution the character
in the movie comes up with is, unfortunately, not a Nash Equilibrium. So what
is it? Well, first things first: what is an equilibrium in the game theoretic
sense of the term?
An equilibrium implies some kind of balanced situation. In
economics and other rational decision-making, equilibria are defined by their
properties. British economist Huw Dixon as described three basic properties of
equilibria: 1) Players’ behavior is consistent. 2) No player has any incentive
to change their behavior. 3) Equilibrium is the stable outcome resulting within
some dynamic process, i.e. the game under consideration.
The simplest explanation of a Nash Equilibrium is by
example: John and Ted are in a Nash equilibrium if John is making the best
decision he can, while also accounting for Ted's decision. At the same time,
Ted is also making the best decision he can, while also accounting for John's
decision. A definition of this concept is as follows: “[Nash’s] theory says
that in non-cooperative games when there are two or more players, and each
player knows what choices the other players face, there is a Nash Equilibrium
if all players have chosen a strategy where they can't benefit by changing
their strategy.” (from Nash
Equilibrium in Economics)
One last important point is that Professor Steven’s lecture
series is mostly conceptual and made for the intelligent layman. It ignores a
lot of complicated mathematical proofs. To illustrate what I mean, here is an
example of the mathematics involved in the proof of
Nash’s Equilibrium. I tried to paste the mathematics, but the characters would not translate to the Blogger post, so please follow the link to the Wikipedia page just to see an example of how complicated the proof is for work like Nash's and why he deservedly received a Nobel for Economics for his work.
Likewise, there is a lot more complicated mathematics involved in computing
the various probabilities in a decision matrix, finding the equilibria of
various kinds in any non-cooperative game, and many other instances. This is
fully disclosed by the instructor. Despite this, the Great Courses lecture
series on Game Theory, Games People Play
is fun, enlightening, and broadens the mind in the understanding of the
complexity of decisions—particularly those facing our business and government
leaders on a daily basis. While I was listening to it, I actually felt smarter!
Then I began to try to summarize the material presented in the lecture series
and felt the opposite effect! I will admit some might find it boring, but if
you enjoy the topic of decision making or complex systems, or if you just enjoy
an intellectual challenge, I can guarantee that you will benefit from at least
a casual listen to this lecture series. As always, happy learning! Work hard to get smarter every day. After all, that is what a learning life is all about!
I would love to hear any of your comments as always.
