Whenever you are hanging
out with your friends and having all your social interactions like, “Where
should we go?” “Who is the best actor?” “Which is the best song?” have you ever
thought about the math or the science behind your decision? This is what Game
Theory is all about. It is the science of decision-making; developed, and put
into limelight, by the great Mathematician John Forbes Nash Jr., who is a Nobel
Laureate (1994).
Forget your preconceptions of what a game is. It is an
interaction between people, where people’s payoff is affected by the decisions
made by others. This definition of game can, without a doubt, be applied on a
game of poke, and also, it can be applied in any practical situation, like at
the end of the article; where you can analyze your decision by making use of game theory.
Game
theory is widely used by mathematicians, economists,
political analysts, biologists, military tacticians, and psychologists, to name
just a few.
Game theory has two main
branches:
1.
Co-operative
2.
Non-cooperative
The first branch emphasizes mainly on the decision
which can affect the whole team or the group of people working on the same
project, or that which is on the same page. Whereas, the second branch mainly
considers the benefits of the individual. In non-cooperative game theory there
will be some winners and there will be some losers, whereas in cooperative
games, there are no losers or winners, but there are payoffs to be calculated
while taking the decisions which would affect the whole group. In these kinds
of situations, we always tend to choose the middle ground which in mathematical
terms satisfies the Nash equilibrium.
So let’s take an example of both the types of game
theory and we will start off with the most famous example of prisoner’s
dilemma. So here is the situation:
There are two
criminals who committed a crime together and were caught. The cops do have
sufficient evidence to put them behind the bars for two years but they don’t
have the required evidence to prove their guilt. So a cop comes with a plan to
put both the criminals in different cells and present them a deal. The deal is
if the 1st criminal confesses the crime his/her sentence would be
pardoned and his/her partner would receive a sentence of 10 years. If both of
them confess to their crime then both the criminals would have a sentence of 5
years.
To sum this up into a table let’s name the two
criminals as:
1.
Ms. Red
MS. RED
|
|||
Silent
|
Confess
|
||
MR. BLUE
|
Silent
|
2 years,
2 years
|
10 years,
0 years
|
Confess
|
0 years,
10 years
|
5 years,
5 years
|
|
So ideally, we
would think that if both the criminals remain silent i.e. if they do not
confess their crime, both of them would be achieve the best-case-scenatio, but
here we should not forget that they are hardened criminals, and hence, they
would see their own benefit before all. So according to game theory, both of
them doing a 5 year sentence is the solution of this problem.
The first state i.e. both
of them being silent is an unstable state and both of them confessing seeing
the lucrative deal is the most stable state.
Co-operative game theory is also known as the
coalition game theory
Here we can have many examples:
1.
The current state government of Jammu and
Kashmir, is led by the coalition of two parties viz. BJP and PDP; both of them
ideologically are polar opposites. BJP believes in integral humanism, and
Hindutva nationalism. Whereas, PDP (People’s Democratic Party) takes a stand
for self-rule in Kashmir, which blindly translates into Free Kashmir. Having a
huge difference in their political ideology and propaganda they did, still,
form a coalition government after a hung assembly result.
2.
Many multi-national and local firms, and
industries came together in one single agenda of Make In India, keeping aside their rivalry and ulterior motives.
In this article I have
only covered the overview of Game Theory and not the mathematical aspect of it.
Do analyze all your
decisions and if you are intrigued by the concept, you can watch the biography
of John Forbes Nash Jr. which is also an Academy award winning film - A
Beautiful Mind.
-Amitkumar
Jha 
