[Maths Class Notes] on Game Theory Pdf for Exam

Based on true logic and analytical decision-making, the theories and steps of Game Theory are applied to various sources in real-life. Both mathematical and non-mathematical fields make use of Game theory to acquire relevant information and make the event a success. Sounds a bit vague but let’s take a deeper look at the concept of Game theory with suitable examples in the following sections.  

Game Theory – Definition and Important Pointers to Learn

Game theory – definition is quite straightforward in its meaning. It is a practical math concept on how a certain game is played using effective strategies. From every point of view, the player’s information such as timing, type of move, the direction of motion, the order of playing, etc. are some of the Game theory’s important determinants. 

The Game theory is based purely on strategic playing. Balancing the diplomatic behaviour along with awareness about the rules of the event and each candidate participating is vital to winning the play.

• On the other hand, the simultaneous game theory involves playing all in 1 go, not accounting the moves or actions of the other player (s).

What is the Theory of Zero-Sum Game?

Zero-sum game or the ‘constant-sum game’ deals with increasing or reducing the resources available during certain games. As the name says, the addition of every strategic combination will sum up to zero (0) only. Hence, the benefits gained by each player adds to zero. So, if 1 opponent wins, the other exact will lose the game. 

Unlike the definition of game theory, here in a zero-sum game, there is an opposition between the interest of 2 players. 

If a player wins the match but it is not probable to state if the other wins or not is termed to be the ‘non-zero-sum game’.

The Applications of Game Theory

• The idea of studying sociological, psychological, and political framework or something or someone, makes the application of game theory important in the field of social sciences like the population census, psychiatry, sociology, social work, etc. 

Not only is the application of game theory defined in the understanding of general behaviour in elements. Even developmental, normative, legal and ethical behaviours and motives are also assessed and judged with better precision using the game theory. 

Let us finally close our learning with a simple example of game theory in the context of the most classic example of history deemed the ‘Prisoner’s Dilemma.’

 

The Classic Instance of Game Theory 

The imaginary case of the Prisoner’s Dilemma involves 2 individuals stealing a vehicle and is held up. Upon further enquiry, it is also found that both the men were involved in a bank robbery issue as well. 2-years imprisonment is going to the judgement here. 

Both the persons were put in different jails. Till now, both the men are suspected for the bank robbery case. Since the prisoners are jailed in 2 separate chambers, the line of communication between the 2 is already cut. 

Now, with the investigation procedures forwarded, the following 2 response situations are about to be given for the 2 prisoners:

• 3-years of imprisonment, if both accused of bank robbery and vehicle theft.

• 1-year imprisonment for the one confessing the truth behind bank robbery. The other unanswered is given the order for 10-years imprisonment. 

The table below includes the possible solutions/outcomes to be expected from both.

 2-CONFESS

 2-DENY

1-CONFESS

 Both punished 3 years

1-DENY

Both punished 2 year

The table displayed above is drawn based on Game theory. And now, the likely choice is to not accept the theft. In that scenario, both the prisoners would serve 2-years imprisonment. However, it is nearly impossible to say whether the other person will confess or not. Hence, the chances are high for both the men to get confessed and serve the 3-years jail sentence.

Conclusion 

Game theory is a practical concept and is regarded as the science of strategies. Game theory involves logic and mathematics. There are 2 forms of playing a game – sequential and simultaneous. Sequential gameplay takes account of the other player’s move and simultaneously is randomly ordered. Fields such as psychology, biology, statistics, social sciences and more use game theory. The ‘Prisoner’s Dilemma’ is the famous case of interpreting the outcomes using game theory.