Introduction to Game Theory

C:\Users\SUMIT\Desktop\bs\game-theory-is-the-science-of-strategy.png

In the Name of the Father, Rebel Without a Cause, Dr. Strangelove, Reservoir Dogs, The Warriors.

Do these movie titles strike a chord with you?

Well these are the movies based on the very interesting game theory.

C:\Users\SUMIT\Desktop\bs\14-126s16.jpg

Hello guys! As promised in my previous writeup, here I’m with a little writeup on Game theory. Hope you all like it. By the way if you haven’t gone through my previous writeup on Nash Equilibrium, kindly go through it, it’s essential.

Let’s come back to your topic:

GAME THEORY

Game theory in a layman’s language depicts a situation in which the decision of a decision maker and its consequences depends/are based on someone else’s decisions.

Simple right?

Now let’s know what a game is all about!

game is a strategic interaction (in economics, social studies, networking, etc) between two or more self-interested agents

Each agent has his/her own opinions and preferences

The outcome of a game depends on what all agents do

  • what actions a game player takes?
  • all users act in the same way?
  • is there a global behaviour pattern?
  • if players can communicate, what effect it will have?
  • repetitions?
  • does it matter if opponents are rational?

Example:

  • Suppose we have two airline companies P1 and P2
  • They are both thinking about opening a new destination
  • Both consider two options: either make tickets cheap or make them expensive
  • Clearly if p1 decides to sell cheap tickets while p2 – to sell expensive tickets, everybody will buy from p1

So, we can depict it with the following pay-off matrix

  • a cell represents consequences of the decision that both players take
p2←
p1↓
500 200
500 (50, 100) (-100, 200)
200 (150, -200) (-10, -10)

 

The following points can be inferred from the above table:

    • if both go for cheap tickets, both will get profits
    • if p2 sells expensive ones and p1 cheap, p1 will get all the profits and p2 will get a loss
    • if both go for expensive tickets, its obvious no one will buy them and subsequently both of them will incur losses.

As it can be seen, it is a variation of the Prisoner’s dilemma. (explained in my previous blog)

It is an example of what we call Normal Game Form. (a type of game form)

So now lets get to the types of game forms.

Image result for poker

  1. Normal Game Form
  2. Extensive Form Game
  3. Mixed-Strategy Game
  4. Repeated Game
  5. Coalitional Game
  6. Bayesian Game

Normal game form is also called as a strategic game.

Preconditions:

Image result for agents cartoon

In game theory, the agents are assumed to be behaving rationally.

  1. Rational agents always try to maximise the consequence.
  2. Few principles are used:
    1. Dominance principle (almost same as unanimity), iterative removal.

[will be discussed in further articles]

    1. Nash equilibrium

Now let’s jot down some examples:

The examples are divided into 3 categories:

  1. Paradoxes
    1. Prisoners dilemma.
  2. Pure competition games
    1. Matching pennies
  3. Cooperation games
    1. Coordination games
  4. General games
    1. Battle of sexes
  5. Other
    1. Cournot Duopoly Model
    2. Bertrand Duopoly Model
    3. Median Voter Theorem (also known as the Allocation Problem)

few examples mentioned above were mentioned and explained in the previous article, click here to read and others will be explained in the upcoming articles.

So, summing it up, these was just a basic introduction on game theory.

I will be trying to cover all relevant topics in the upcoming blogs.

So that’s all for now!

Hope you liked reading the articles. Any issues or clarifications or discussions, kindly do reach me: sumitpradhan.kumar@gmail.com.

Thank you, stay tuned.

Image result for game theory cartoon

 

You may also like...

Leave a Reply

Your email address will not be published. Required fields are marked *