A Nash equilibrium is an outcome where no player regrets his move given his opponent’s strategy.
A Nash equilibrium is a powerful game theory tool because it shows when an outcome is stable; it shows outcomes where no player wants to change his strategy.
When trying to move to a new equilibrium, you should consider if the new outcome would be a Nash equilibrium. If it’s not, then your new outcome is unstable and might be difficult to achieve.
Seeing the movie A Beautiful Mind will not increase your knowledge of game theory.