# Game Theory

Game theory is a mathematical theory that studies principles of decision-making in situations where several parties interact with each other.

## Overview of Game Theory

The game theory was first developed by John von Neumann, who was a mathematician, and Oskar Morgenstern, a German-American economist, in the 1940s. Besides, mathematician John Nash is determined as their successor as he contributed a lot in the development of their work.

The central point of it is the game that presents a model of a strategic interaction among independent players. The crucial moment here is that decisions made by one person affect the choices of others and the outcome of the interaction as a whole.

The game recognizes the types of the people involved in it, what they prefer, possible strategies and what impact they have on the result of the situation.

Game theory can be applied in many fields, such as psychology, politics and others.

## Key Terms

When there is a situation in which two or more sides are involved, we can rely on this concept to predict the possible results of the situation.

**Here are the key terms:**

- Game: A model in which steps of the players have an influence on the outcome.
- Players: A person who is in charge of taking actions.
- Strategy: Scenario for all possible situations that may come up in the process.
- Payoff: Benefit that a side gets after it achieves a result.
- Information set: The facts that a person can know at a particular time of the game.
- Equilibrium: The stage when both sides agree on the actions to be taken and they achieve the final result.

## What is the Nash Equilibrium

It is the final stage of the game when none of the players can derive more benefit by changing the actions unilaterally.

In many situations the Nash equilibrium can be found after a while. Nevertheless, if you have reached it, you can’t digress from it.

As a rule, there are two or even more equilibriums in such interactions. Nevertheless, it happens only when more complicated elements than two choices by two sides are presented.

## Main Types

**The most frequently mentioned types of game theories are**:

**cooperative**(studies games in which groups of players — coalitions — can combine their efforts, here they are only aware of the payoffs);**non-cooperative**(examines how rational players interact with each other in order to reach a goal).

The most popular game is the strategic game, in which the possible strategies and the results that come from a set of choices are enumerated. One of the examples that you can observe in real life is a rock-paper-scissors game.

## 4 Real Examples

Below are listed several outstanding examples of cases that the game theory studies.

**The Prisoner's Dilemma**. It’s a classic example of the discipline which will help us understand the basic principles of the theory. The game considers two players who are both suspected of a crime. Prosecutors have found only circumstantial evidence to prove that they are guilty. That’s why the officials offer a plea deal to the prisoners – to confess and betray the other prisoner.

If A confesses and B remains silent, B will be punished by a term of imprisonment of 3 years and A will be imprisoned for 9 years. If B confesses and A doesn’t, A will be punished by a term of imprisonment of 10 years and B will get 2 years. If both make a deal, each prisoner will be sentenced to prison for 5 years. However, if both remain silent, they will get 2 years.

The best tactic is to keep quiet as the prisoners are in different cells and they cannot conspire with each other.

**Dictator Game**. In this game side A should think about how to share prize money with side B. This strategy helps have a clear understanding of the way people behave. The study showed that 50% of people saved money for themselves, 5 % distributed money equally, about 45% gave the other player a smaller part of the winning.

**Volunteer’s Dilemma**. It is a situation in which each player can either make a small sacrifice for mutual benefit, or hope that anyone else will volunteer. For instance, power supply of the entire district has been disconnected. The residents know that the electric power company will solve the problem if at least one person notifies them for a fee. If no one volunteers, this is the worst outcome for all participants. If someone chooses to be a volunteer, the rest will benefit from it.

**The Centipede Game**. In this case two sides alternately have an opportunity to take a bigger share from money stash that is continuously becoming larger in amount. If side A passes the stash to the side B and it takes it, side A gets less money than if it had taken the stash.

The game ends if a player receives the stash and he has a larger portion. On the other hand, the second player receives a small portion. There is a certain number of rounds and each side is aware of that number.