What is Nash Equilibrium?

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Nash equilibrium is a concept in game theory where the optimal outcome is when there is no incentive for players to deviate from their initial strategy. The players have knowledge of their opponent’s strategy and still will not deviate from their initial chosen strategies because it remains the optimal strategy for each player.Overall, an individual can receive no incremental benefit from changing actions, assuming that other players remain constant in their strategies. A game may have multiple Nash equilibria or none at all.

Definition

Nash Equilibrium is a concept in game theory where players reach an optimal outcome when no player has an incentive to deviate from their initial strategy. Players are aware of their opponents' strategies but still do not deviate from their initial choice because it remains the optimal strategy for each player. Essentially, assuming other players' strategies remain unchanged, an individual cannot gain additional benefits by changing their behavior.

Origin

Nash Equilibrium was introduced by John Nash in the 1950s, laying the foundation for the development of game theory. Nash's work was recognized with the Nobel Prize in Economics in 1994, highlighting the concept's significance in economics and other social sciences.

Categories and Features

Nash Equilibrium can be divided into pure strategy Nash Equilibrium and mixed strategy Nash Equilibrium. Pure strategy Nash Equilibrium involves players choosing a definite strategy, while mixed strategy Nash Equilibrium involves players randomly selecting among multiple strategies. Pure strategy equilibria are often easier to identify, but in some complex games, mixed strategy equilibria may be more common. A key feature of Nash Equilibrium is stability, meaning that in equilibrium, no single player has an incentive to unilaterally change their strategy.

Case Studies

A classic example is the Prisoner's Dilemma. In this game, two suspects are interrogated separately; if both remain silent, they receive a lighter sentence; if one betrays the other, the betrayer is released while the other receives a heavy sentence; if both betray, they receive a moderate sentence. The Nash Equilibrium in this scenario is for both to betray, as this is the optimal strategy for each individual, even though cooperation would yield a better collective outcome.

Another example is a price war in market competition. Suppose two companies compete in a market; if one company lowers its prices, the other will follow suit to maintain market share. Ultimately, the Nash Equilibrium might be for both companies not to lower prices, as doing so would lead to reduced profits.

Common Issues

Investors applying Nash Equilibrium may encounter issues such as the complexity of identifying equilibrium points, especially in games with multiple players or complex strategies. Additionally, Nash Equilibrium does not always lead to the optimal collective outcome, which can lead to misconceptions that equilibrium states are always the best choice.

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