By Krisha Shah

**Nash equilibrium** is a fundamental concept in the theory of games and the most widely used method of predicting the outcome of a strategic interaction in the social sciences. A game (in strategic or normal form) consists of the following three elements: a set of players, a set of actions (or pure-strategies) available to each player, and a payoff (or utility) function for each player. The payoff functions represent each player’s preferences over action profiles, where an action profile is simply a list of actions, one for each player. A pure-strategy Nash equilibrium is an action profile with the property that no single player can obtain a higher payoff by deviating unilaterally from this profile.

We take an example below for better understanding, this situation is also called as the *prisoner’s dilemma*. Let’s take two prisoners who have been caught by the police for carrying out an horrific crime. Their names are Ms. Red and Mr. Blue. The police thought of a strategy through which they could make the prisoners confess the crime. So for that they took them into a room separately without any communication taken place. Both of them were asked to admit the crime of the other person. And a few options where given if they confess that the other person has done the crime then you get 0 years of jail and the other person gets 3 years of jail and vice versa is possible if your partner admits your crime then you get 3 years of jail and he gets none. But if none of you confess the crime then you both get only 1 year of jail, and as it happens in ideal situation if both of you confess the crime then both of you shall get 2 years of jail.

As both are rational agents the ideal way to save themselves from maximum punishment is by confessing as it gets you only 2 years of jail rather than 3 years. Unless without confessing both stay silent and get only 1 year of jail.

The prisoner’s dilemma is a paradox in decision analysis in which two individuals acting in their own self-interests do not produce the optimal outcome. The typical prisoner’s dilemma is set up in such a way that both parties choose to protect themselves at the expense of the other participant. As a result, both participants find themselves in a worse state than if they had cooperated with each other in the decision-making process. The prisoner’s dilemma is one of the most well-known concepts in modern game theory.

### Understanding the Nash Equilibrium:

Nash equilibrium is named after its inventor, John Nash, an American mathematician. It is considered one of the most important concepts of game theory, which attempts to determine mathematically and logically the actions that participants of a game should take to secure the best outcomes for themselves. The reason why Nash equilibrium is considered such an important concept of game theory relates to its applicability. The Nash equilibrium can be incorporated into a wide range of disciplines, from economics to the social sciences.

References:

https://www.investopedia.com/terms/n/nash-equilibrium.asp