Today I will be writing
about Game Theory. You may ask “why should anybody write about something
like that? “Well, since I was at University I have been captivated by
Game Theory and its applications to real life conflicts. Recently, I had the
opportunity to enroll a seven week long online course.
If you think Game
Theory has something to do with complicated mathematic algorithms, impossible
formulas, and so forth, you are very wrong!! I won´t say you won´t need any
numerical background to understand Game Theory but I can definitely assure you,
that you don´t need to be Stephen Hawkins to learn the basics.
Game theory is the study of strategic
decision making. More formally, it is "the study of mathematical models of
conflict and cooperation between intelligent rational decision makers"
game theory has been used to study a wide variety of human and animal
behaviors. It was initially developed in economics to understand a large
collection of economic behaviors, but the use of game theory in the social
sciences has expanded, and game theory has been applied to political,
sociological, and psychological behaviors as well.
A game consists of a set
of players, a set of strategies available to those players, and a set of
payoffs for each combination of strategies.
There are several types
of games, but the most common are:
Cooperative/ Non
cooperative: A game is cooperative if the players are able to
form binding commitments and it´s non cooperative if this is not possible.
Symmetric/ Non
symmetric: A symmetric game is a
game where the payoffs for playing a particular strategy depend only on the
other strategies employed, not on who is playing them. We can say that if the
identities of the players can be changed without changing the payoff to the
strategies, then a game is symmetric.
Zero sum/ No zero sum: In
zero-sum games the total benefit to all players in the game, always adds to
zero. In the other hand, non-zero-sum games has net results greater or less
than zero.
Simultaneous/
Sequential: In simultaneous games
both players move simultaneously, or if they do not move simultaneously, the
second player is unaware of the first players' actions. In sequential games
later players have some knowledge about earlier actions instead.
Perfect/ Imperfect
information: A game is one of
perfect information if all players know the moves previously made by all other
players. Therefore, only sequential games can be games of perfect information
because players in simultaneous games do not know the actions of the other
players.
Now we know some of the
existing types of games, let´s see the different strategies that a player can
choose to play:
Pure
strategy: It
determines the move a player will make for any situation he or she could face.
Mixed
strategy:
It is
an assignment of a probability to each pure strategy. This allows for a player
to randomly select a pure strategy.
Totally
mixed strategy: It is a mixed strategy in which the player assigns a
strictly positive probability to every pure strategy.
Finally
it is important to understand the concept of Nash Equilibrium.
Nash
equilibrium:
It is a solution of a non-cooperative game in which each player is assumed to
know the equilibrium strategies of the other players, and no player has
anything to gain by changing only his own strategy unilaterally.
Let´s have a look now at
what it´s the best known example of games theory: The Prisoners Dilemma.
Two prisoners, there is no
evidence to convict either one therefore the prosecutor seeks a confession.
Each prisoner has two strategies:
-
Prisoner 1:
Confess, no confess
-
Prisoner 2:
Confess, no confess
It is known that
strategies are chosen simultaneously by the two prisoners and with no
communication between them.
Below you can see the
matrix and the payoffs depending on the decisions made.
Here,
regardless of what the other decides, each prisoner gets a higher pay-off by
betraying the other. Prisoner A can state that no matter what prisoner B
chooses, prisoner A is better defecting than cooperating. As a result, based on
the payoffs above, prisoner A should logically betray prisoner B. The game is
symmetric, so Prisoner B should act the same way. Since both rationally decide
to defect, each receives a lower reward than if both were to stay quiet. That
strategy results in both players being worse than if each have chosen to keep
quiet at the cost of spending more time in jail himself.
There are plenty more examples
you can check if you want to get more information about Game Theory. I
encourage you to check the following links, where more information and examples
are available:
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