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Nash Equilibrium in Economics: Definition & Examples

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  • 0:03 Introduction to the…
  • 1:55 The Prisoner's Dilemma
  • 3:26 Lesson Summary
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Lesson Transcript
Instructor: Wren Hawthorne
The Nash Equilibrium is an important concept in economics, especially in the field of game theory. In this lesson, we will learn about the Nash Equilibrium and follow up with a quiz.

Introduction to the Nash Equilibrium

You may recognize the name John Nash if you've ever seen the Academy Award-winning 2001 movie A Beautiful Mind. In the film, Nash is portrayed by actor Russell Crow. The film highlights Nash's brilliance in the field of game theory and mathematics and also his battle with schizophrenia.

John Forbes Nash was born on June 13, 1928. He was a professor at Princeton University and received the 1994 Nobel Memorial Prize in Economic Sciences for his work in game theory and particularly the ideas behind the Nash Equilibrium.

John Nash

In A Beautiful Mind, there is a fictionalized scene that depicts the origins of the Nash Equilibrium. John Nash and several of his fellow Princeton students are in a bar when a beautiful blonde woman walks in with her friends. Nash and his gang want to introduce themselves to her. One of his friends references Adam Smith and elaborates on Smith's concept that with competition the most worthy of them will rise to the top.

At this point in the movie, Nash says that Adam Smith has it wrong, that there is a better solution to the dilemma than just pure competition. He says that if they all approach the blonde, she will turn every one of them down. Then her friends will also turn them down because they wouldn't want to play second fiddle. But if they approach her friends instead (and not the blonde), they will all find a more favorable solution.

Though the movie takes some creative liberties, this scene partially illustrates Nash's concept that would develop into an entirely new thought in economics. His theory says that in a non-cooperative game when there are two or more players and each player knows what choices the other players face, there is a Nash Equilibrium if all players have chosen a strategy and can't benefit by changing their strategy.

The Prisoner's Dilemma

The best way to demonstrate a Nash equilibrium is through an example called the Prisoner's Dilemma. Let's say that you and an acquaintance, who we'll call Harry, have been picked up for petty theft. The police have the evidence to convict both of you, and you will both serve a jail sentence of 2 years.

However, the police have suspicion that both of you were part of a much larger bank robbery but do not have enough evidence to convict either of you. So, the DA decides to give you and Harry an incentive to snitch on the other person about the bank robbery. They put both of you in separate rooms (which is the non-cooperative part of the game). If you snitch on Harry and he doesn't snitch on you, you get off with 1 year and he will receive 7 years. He is given the same deal. However, if you both end up snitching, you will both receive 4 years (see Table 1 below).

Table 1. Prisoner's Dilemma

Prisoner

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