Recently I noticed in movies and TV shows, game theory is
being mentioned and it struck me that I don’t know what game theory is. So here
I am researching it and sharing what I learned with you. First, let me say that
there is so much more to game theory than what I can write about without being
long winded or boring. I will only cover the basics. That being said, here we
go. Game theory is the study of mathematical models of conflicts and
cooperation between intelligent rational decision makers. It is mainly used in
economics, political science and psychology. It can also be applied to logic,
computer science and biology.
The first known discussion of game theory occurred in letter
to James Waldegrave, a British diplomat from Charles Waldegrave, his uncle, in
1713. Known as the Waldegrave problem, it was a mixed strategy solution to a
two-person card game called le Her in which a standard deck of 52 cards are
played between a dealer and a receiver. James Madison used what is now called
game theoretic analysis to predict how the states can be expect to act under
different taxation systems (Vice of the
Political System of the United States, April 1787). Throughout the years,
many other theories devised their own game theories. In 1838, Antoine Augustin
Cournot used duopoly, a form of oligopoly where only two sellers exist in one
market, and presented a solution to the Nash equilibrium. The Nash equilibrium
is a solution concept of a non-cooperative game. The study of game theory
didn’t truly exist as its own field until 1938. While there are many game types
in game theory, I will be discussing three.
First, cooperative versus non-cooperative games. In
cooperative game theory, players are able to form binding commitments
externally enforced, i.e. contract law. The focus is on predicting which
coalitions will form place and the resulting payoffs. Cooperative game theory
does not focus on how coalitions achieve their payoffs. For example, a
coalition can exchange whatever it wants among its members; however, it does
not discuss how offers or counteroffers are made. The image of a bargaining
table in which two or more people are hashing out a business deal or even a
criminal plea deal. Non-cooperative game theory, players cannot form alliances
or if all agreements need to be self-enforcing, i.e. credible threats. The
focus is on predicting individual players’ actions and the possible payoffs
while trying to predict what strategies the players will choose. In essence how
people should or do act for the maximum individual benefit.
Second, symmetric versus asymmetric game theory. In symmetric
game theory, payoffs for playing a particular strategy depends only on the
other strategies played and not who played them. If the players changed without
changing the strategies, the playoffs would be the same. The game of chicken is
an example of a symmetric game. Each player has two decisions to yield or not. Regardless
who yields and who doesn’t, the payoff is the same. If one player yields, the
other player should not yield. If one player won’t yield, the other player
should. In asymmetric game theory, there are no identical strategy sets for
both players. For example, the ultimatum game which is used in economic
experiments. One player receives a sum of money and proposes how to divide the
money. If player two accepts the proposal, the money is split according to the
proposal. If player two rejects the proposal, neither player receives any
money.
Third, zero sum versus non zero sum game theory. In zero sum
game theory, the choices made by the players can neither increase nor decrease
the available resources. The total benefit to all players always adds to zero.
In other words, a player only benefits at the expense of another. Chess is an
example of a zero sum game as one player benefits when the other player loses a
piece or cannot make another move. In a non-zero sum game, the outcomes results
are greater or less than zero. A gain by one player does not necessarily
correspond with another player’s loss. In layman’s terms, it is a win-win
situation. One example is The Prisoner’s Dilemma. It is the problem faced by
two accomplices locked in separate cells. Each is offered three choices by the
police: one, they can both confess to the charges, both will be jailed for five
years. Two, if only one confesses, he will be freed but the non-confessor will
be jailed for ten years. Or three, if neither confesses, both will be tried for
a minor offense and will be jailed for one year. If both prisoners know that
the other will not confess, neither will confess and serve one year in jail. It’s
a win-win for both prisoners.
In conclusion, game theory is, at its core, about
prediction. Predictions of behavior, strategies, decision making and payoffs. It
is about keeping an equilibrium or balance. It is about human conflicts and
cooperation within competitive or game situations. It is about optimal decision
making for the best outcomes for all involved or one individual over another. The
theory is applied to many games we play: chicken, chess, poker and other
situations where decisions are made for the best outcomes. It is a very simplified
explanation and only hits the tip of the iceberg when it comes to what game
theory is and how it is used. I’m curious to read further and hope it was
informative for you, if you were unaware of what game theory is.
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