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What is Game Theory?

In Our real life there are many conflicts between people or groups of people.Some problems are political ,some are business related and some are personal and so on.This problem occurs when there are two parties of oposing interests.Then those problems need co-operation among the participating parties.For example the coalition of two or more parties in running a same business.Game theory is a way of analyzing such situations

Pure Strategy:

Pure strategy for a player is a description of the decsions he is going to make at all situations that can arise in the game.That will tell the player what to do at any situation after his opponent has taken some decsions.It is very important to identify the pure strategy of any game otherwise the result will not be accurate.

Payoff Matrix:

Another way to explain a game is to list all possible pure strategies of the players,I-1,I-2,….I-p for player-I and II-1,II-2,…..II-q for player-II and then find the payoff m-ij to player-I when player-I uses his ith pure strategies I-I and player -II uses his jth strategies II-j(i=1,2,…,p,j=1,2,…..q) continuously.In this case there is a chance for player-I to have more payoff interpreted as expected payoff.This the payoff matrix of the game.p*q matrix A=(m-ij) is known as the payoff matrix.
Now i will discuss the most common game in our day to day life.I will draw the game tree and write all the pure strategies and payoff matrix of the game.

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Matching Coin:

Two player will participate in this game.They are player-I and player-II.Each will have a coin and they will display them constantly.Coin has two ends one end is head and another end is tail.If both the players coin are matched that means both are heads or both are tails then player-II wins.And he will receive a payoff from player-I.If both are not heads or tails then player-II loses and he has to pay a unit payoff to player-1.

Game Tree:

The game tree of this game are presented below.

We observe from the game tree that each of the players have two pure strategies.They are,
I-1:Choose Head
I-2:Choose Tail
II-1:Choose Head
II-2:Choose Tail

The payoff matrix is:

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