306 CHAPTER 13 | Oligopoly: Firms in Less Competitive Markets
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Extra Making
the
Connection
A Beautiful Mind: Game Theory Goes to the Movies
John Nash is the most celebrated game theorist in the world, partly because of his achievements and
partly because of his dramatic life. In 1948, at the age of 20, Nash received bachelor’s and master’s
degrees in mathematics from the Carnegie Institute of Technology (now known as Carnegie Mellon
University). Two years later, he received a Ph.D. from Princeton for his 27-page dissertation on game
theory. It was in this dissertation that he first discussed the concept that became known as the Nash
equilibrium. Nash appeared to be on his way to a brilliant academic career until he developed
schizophrenia in the 1950s. He spent decades in and out of mental hospitals. During these years, he
roamed the Princeton campus, covering blackboards in unused classrooms with indecipherable writings.
He became known as the “Phantom of Fine Hall.” In the 1970s, Nash gradually began to recover. In 1994,
he shared the Nobel Prize in Economics with John Harsanyi of the University of California, Berkeley, and
Reinhard Selten of Rheinische Friedrich–Wilhelms Universität, Germany, for his work on game theory.
In 1998, Sylvia Nasar of the New York Times wrote a biography of Nash, titled A Beautiful Mind. Three
years later, the book was adapted into an award-winning film starring Russell Crowe. Unfortunately, the
(fictitious) scene in the film that shows Nash discovering the idea of Nash equilibrium misstates the
concept. In the scene, Nash is in a bar with several friends when four women with brown hair and one
with blonde hair walk in. Nash and all of his friends prefer the blonde to the brunettes. One of Nash’s
friends points out that if they all compete for the blonde, they are unlikely to get her. In competing for the
blonde, they will also insult the brunettes, with the result that none of them will end up with a date. Nash
then gets a sudden insight. He suggests that they ignore the blonde and each approach one of the
brunettes. That is the only way, he argues, that each of them will end up with a date.
Nash immediately claims that this is also an economic insight. He points out that Adam Smith had argued
that the best result comes from everyone in the group doing what’s best for himself. Nash argues,
however, “The best result comes from everyone in the group doing what’s best for himself and the
group.” But this is not an accurate description of the Nash equilibrium. As we have seen, in a Nash
equilibrium, each player uses a strategy that will make him as well off as possible, given the strategies of
the other players. The bar situation would not be a Nash equilibrium. Once the other men have chosen a
brunette, each man will have an incentive to switch from the brunette he initially chose to the blonde.
Question: Convert the scene from the bar into a game. There are two players John and Steve. They each
have the same possible strategies: “approach the blonde” or “approach the brunette.” Think of the payoffs
in the matrices as measures of utility. Choose payoffs so that there is no Nash equilibrium.
Answer: John’s payoffs appear first in each cell. For example, if both John and Steve approach the
blonde, John receives 12 utils and Steve receives 11 utils. Whichever cell they initially start in, at least
one of them has incentive to change his choice—that is, approach the blonde if he initially approached the
brunette, or approach the brunette if he initially approached the blonde. Therefore, the game does not
have a Nash equilibrium.
A Note on the Bar Scene in A Beautiful Mind
The Extra Making the Connection: A Beautiful Mind: Game Theory Goes to the Movies suggests
that “the bar scene” in the Ron Howard movie A Beautiful Mind misstates the concept of the Nash
equilibrium because it does not represent a mutual best response. The Making the Connection also