Explaining a Cornerstone of Game Theory: John Nash’s Equilibrium
John F. Nash Jr. was an American mathematician with tremendous contributions in game theory. However, the game theory was invented by John Von Neumann. The game theory attempts to look at the decision making in situations of a variety of competitions. It can be applied to economics, biology, political science, as well as computer science, and many other fields. The game is organized into several players, and each player has a set of strategies and he/she will aim to maximize their payoff in the game under different circumstances.
One of the most significant concepts in game theory is the Nash Equilibrium, which was introduced by John Nash. As we studied in class, the Nash Equilibrium is the solution in the game where there exists no incentive for the players to change their strategies regardless of the strategies of other players. The Nash Equilibrium is considered as the cornerstone of the game theory. The article mainly discusses about the basic notion of Nash Equilibrium and how it can be applied to the situation in real life. It also introduced and analyzed the Prisoner’s Dilemma that we have talked in lecture.
The article also talks about the movie, “A Beautiful Mind”, which was based on Dr. Nash’s early life. There is a scene in the film that describes how Dr.Nash came up with the concept of the game theory. In the movie, Dr.Nash was with three of his friends at a D-bar. And they saw a blond lady and four of her brunette friends coming in to the bar. The problem here is that all of them including Dr.Nash preferred the blond woman. If they went after the blond and got rejected, four brunettes would possiblly reject them as well since no one likes to be the second choice. Thus, Dr.Nash suggested that they should chase after the brunettes and ignore the blond woman instead. “We don’t get in each others’ way and we don’t insult the other girls. That is the only way we win.”, stated by Dr.Nash in the movie. However, this strategy here does not necessarily represent a Nash Equilibrium. But it illustrates the importance of game theory and Nash Equilibrium in real life.