# Game Theory

Game theory is a Mathematical subject that is commonly used in practical life. It is applied to various other non-mathematical fields too. Game theory explains how a strategic game is played. It determines the way or order in which the players should make moves. It considers the information for the players at each decision point.

In-game theory, the interdependence of actions of players is the essence of the game. The game has two kinds of strategic interdependence – one is sequential, and the other is simultaneous. In sequential interdependence, players act in a sequence, aware of other players actions. While, in simultaneous interdependence, players act at the same time, ignoring other players’ actions. The game theory is all about such strategies. Let us go ahead and learn more about game theory.

## Game Theory Definition

The game theory is said to be the science of strategies which comes under the probability distribution. It determines logical as well as mathematical actions that should be taken by the players in order to obtain the best possible outcomes for themselves in the games. The games studied in game theory may range from chess to tennis and from child-rearing to takeovers. But there is one thing common that such an array of games is interdependent, i.e. outcome for each player depends upon the strategies of all.

In other words, game theory deals with mathematical models of cooperation and conflicts between rational decision-makers. Game theory can be defined as the study of decision-making in which the players must make strategies affecting the interests of other players.

## Zero-Sum Game Theory

There is a special kind of game studied in game theory, called zero-sum games. They are constant-sum games. In such games, the available resources can neither be increased nor decreased. Also, the total benefit in zero-sum games for all combination of strategies, always adds to zero. We can say that in zero-sum games, one wins and exactly one opponent loses. The sum of benefits of all the players for any outcome is equal to zero is called a zero-sum game. Thus, the interest of the two players is opposed.

Several games, game theory are non-zero-sum games, since net result of outcome is less than or greater than zero. So, when one player’s gain does not correspond to other’s loss, it is called a non-zero sum game.

## Game Theory Applications

The game theory is widely applied to study human as well as animal behaviours. It is utilized in economics to understand the economic behaviours, such as behaviours of consumers, markets and firms. Game theory has been commonly used in social sciences as well. It is applied in the study of sociological, political and psychological behaviours. The use of analysis based on game theory is seen in biology too. In addition to behavioural prediction, game theory utilized in the development of theories of normative or ethical behaviour.

### Game Theory Example

The best example of game theory is a classical hypothesis called “Prisoners Dilemma”. According to this situation, two people are supposed to be arrested for stealing a car. They have to serve 2-year imprisonment for this. But, the police also suspects that these two people have also committed a bank robbery. The police placed each prisoner in a separate cell. Both of them are told that they are suspects of being bank robbers. They are inquired separately and are not able to communicate with each other.

The prisoners are given two situations:

• If they both confess to being bank robbers, then each will serve 3-year imprisonment for both car theft and robbery.
• If only one of them confesses to being a bank robber and the other does not, then the person who confesses will serve 1-year and others will serve 10-year imprisonment.

According to game theory, the prisoners will either confess or deny the bank robbery. So, there are four possible outcomes :

 2-Confess 2-Deny 1-Confess Both punished 3 years Prisoner 1 punished 1 year Prisoner 2 punished 10 years 1-Deny Prisoner 1 punished 10 year Prisoner 2 punished 1 year Both punished 2 years

Here, the best option is to deny. In this case, both will have to serve 2 years sentence. But it cannot be guaranteed that others would not confess, therefore most likely both of them would confess and serve the 3-year sentence.

Register with BYJU’S – The Learning App and also explore the videos to learn with ease.