Game Theory: Overview, Questions, Preparation

This theory is a part of a probability distribution. This theory plays a major role in the decision-making process. It determines how a player moves and what his mind thinks.

Zero-Sum Game Theory

There are closed games in which the outcome is fixed. The resources of this game can neither be decreased nor increased. The total benefit is always zero. The result of this game is that one wins and the other always loses. 

Whereas when one player’s game does not correspond to another player’s loss, it is termed a non-zero-sum game.

Game Theory Examples 

One of the best examples to understand game theory in a practical way. There are two prisoners in two separate cells. Both can be imprisoned for a minor offence, but not for a major offence unless then testify against each other. Following are the possibilities –

1. If both of them confess, they will be imprisoned for major offence and get 9 years in prison.
2. If none of them confesses, they will be imprisoned for a minor offence and get only 1 year in prison.
3. If prisoner 1 confesses and prisoner 2 does not, then prisoner 1 will get 9 years in prison, whereas prisoners 2 will get only 1 year.
4. If prisoner 2 confesses and prisoner 1 does not, then prisoner 2 will get 9 years in prison, whereas prisoners 1 will get only 1 year.

Game theory suggests that both of them should not confess and that’s how they will get minimum imprisonment.  

Game theory has vital importance in the probability field. This branch of probability helps a great deal in solving dilemma questions and coming towards the outcome.
Approximately 10 marks are allocated to the entire probability chapter. Out of which 5-6 marks, questions are expected out of the game theory topic. A mix of 3-5 MCQ and short answer type questions are expected from this topic. 

Question 1. Four students – A, B, C, and D are sitting in random order next. Find the probability that B sits at the Northeast corner of the room.

Solution. To make 4 students sit at 4 corners of the room, there are 24 different ways. B sits at the northeast corner of the room – there are 6 different ways to it. 

Thus, the required probability is = 6/24 = ¼

Question 2. Identify the probability of getting at least 1 heads, when the coin is thrown three times?  

Solution. Sample Space: HHH,TTT,TTH,HTT,THT,THH,THH,HTH = 8

Required Probability = 1-1/8 = 7/8

Question 3. 12 People are sitting together on a table. Find out how 2 particular people are sitting next to each other?

Solution. 12 people can sit in 11 different ways.

No. of ways in which 2 people can sit together are = 10! * 2!

Required probability = 10! * 2! / 11! = 2/11

Q: What is a zero-sum game?

Q: How are game theory models classified?

Q: How is a game fair?

Q: What happens when the maximum and minimum values of the game are the same?

Q: How can a mixed strategy game be solved?

Q: When no saddle point is found in a game’s payoff matrix, how will the game’s value be found?