Nash Equilibrium
Nash Equilibrium
A Nash Equilibrium is a solution concept in Game Theory where no player can benefit by changing their strategy while the other players keep their strategies unchanged. In other words, each player’s strategy is optimal given the strategies of all other players.
Examples:
- Prisoner’s Dilemma: Two criminals are arrested and interrogated separately. If both remain silent, they each serve 1 year. If one betrays the other, the betrayer goes free while the other serves 3 years. If both betray, they each serve 2 years. The Nash Equilibrium occurs when both betray each other, as neither can reduce their sentence by unilaterally changing their strategy.
- Traffic Flow: Consider two routes to a destination. If most drivers choose Route A, it becomes congested, making Route B faster. However, if too many switch to Route B, it can become congested as well. The Nash Equilibrium is achieved when drivers distribute themselves between the two routes in such a way that no one can reduce their travel time by Switching routes.
Cases:
- Cournot Competition: In a market with two firms deciding on quantities to produce, the Nash Equilibrium occurs when each firm chooses a quantity that maximizes its profit, given the quantity chosen by the other firm.
- Battle of the Sexes: A couple wants to go out but prefers different activities. The Nash Equilibrium is achieved when they choose to go to an event that satisfies one partner’s preference while still reaching a compromise.