Sadly John Nash, the Nobel Prize-winning mathematician whose life story was the subject of the Academy Award-winning film “A Beautiful Mind” died yesterday in a car crash – his wife Alicia was also killed. Best known for advances in game theory, which is essentially the study of how to come up with a winning strategy in the game of life — especially when you do not know what your competitors are doing and the choices do not always look promising.
From 1930 to 1940 mathematician John von Neumann did the pioneering work to establish the field of game theory although Nash extended the analysis beyond zero-sum, I-win-you-lose types of games to more complex situations in which all of the players could gain, or all could lose.
In game theory, the Nash equilibrium is a solution concept of a non-cooperative game involving two or more players, in which each player is assumed to know the equilibrium strategies of the other players, and no player has anything to gain by changing only their own strategy.
The film “A Beautiful Mind,” based on Dr. Nash’s life, tries to explain game theory in a scene in which Russell Crowe, playing Dr. Nash, is at a bar with three friends, and they are all enraptured by a beautiful blond woman who walks in with four brunette friends – see video below.
While his friends banter about which of them would successfully woo the blonde, Dr. Nash concludes they should do the opposite: Ignore her. “If we all go for the blonde,” he says, “we block each other and not a single one of us is going to get her. So then we go for her friends, but they will all give us the cold shoulder because nobody likes to be second choice. But what if no one goes to the blonde? We don’t get in each other’s way and we don’t insult the other girls. That’s the only way we win.”
While this never-happened-in-real-life episode illustrates some of the machinations that game theorists consider, it is not an example of a Nash equilibrium.