Nash Equilibrium: Definition and Examples - Deepstash
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What is Nash Equilibrium?

What is Nash Equilibrium?

It is a concept in game theory in which every participant in a noncooperative game can optimize their outcome based on the other players’ decisions.

Nash equilibrium is achieved in a game when no player has any incentive for deviating from their own strategy, even if they know the other players’ strategies.

In economic theory, it is used to illustrate that decision-making is a system of strategic interactions based on the actions of other players. It can be used to model economic behavior to predict the best response to any given situation.


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Example: Battle of the sexes

Example: Battle of the sexes

A man and a woman are hoping to attend an event together, but they must choose between a prizefight or a ballet.

They cannot communicate where they will go beforehand, and the man in this story would prefer to go to the prizefight while the woman in this scenario would like to go to the ballet.

This game has two unique Nash equilibrium strategies: one in which they both go to the prizefight and one in which they both go to the ballet.


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How to Find Nash Equilibrium

How to Find Nash Equilibrium

To find it, share each player’s strategy with every other player. If the players do not change their strategies, you have found the Nash equilibrium.

For eg, in the battle of the sexes scenario, draw a table with two rows and two columns. 

The vertical axis represents the woman’s options: ballet/prizefight and horizontal axis represents the man’s choices: also ballet /prizefight. In the top left quadrant, they both choose ballet (Nash Equilibrium). In the bottom right quadrant, they both choose prizefight (Nash Equilibrium). This table illustrates there are two possible Nash equilibria.


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