Nash Equilibrium

Published Oct 25, 2023

Definition of Nash Equilibrium

Nash Equilibrium is a concept in game theory that refers to a situation in which each player in a game makes the best decision given the decisions of the other players. In other words, no player has an incentive to unilaterally change their strategy because doing so would not improve their outcome. It is named after John Nash, a Nobel Prize-winning mathematician and economist who developed this concept.

Example

Consider a classic example of the Prisoner’s Dilemma. Two individuals, Alice and Bob, are being held in separate cells and are being questioned about a crime they allegedly committed together. The police offer each of them a deal: if one stays silent and the other confesses, the one who confesses will get a reduced sentence while the one who stayed silent will face a harsher punishment. If both of them confess, they will both receive a moderate sentence. If both of them stay silent, they will both get a minimal sentence.

In this scenario, the Nash Equilibrium occurs when both Alice and Bob confess. If Alice stays silent while Bob confesses, Alice faces a harsher punishment, so it is in her best interest to confess. The same logic applies to Bob. Therefore, both players have no incentive to deviate from confessing, resulting in a Nash Equilibrium.

Why Nash Equilibrium Matters

Nash Equilibrium is an important concept in game theory as it helps predict the outcomes of strategic interactions. Understanding Nash Equilibrium can be useful in various fields such as economics, politics, and business negotiations. It provides insights into how rational individuals or organizations make decisions in competitive situations, taking into account the decisions made by others. By identifying Nash Equilibrium, individuals can make informed decisions to maximize their outcomes and avoid suboptimal choices.