What a Beautiful Mind Left Behind
(San Francisco Chronicle Op-Ed, May 28, 2015)
The death of John Nash and his wife Alicia from a tragic automobile accident in New Jersey last weekend stunned those of us who study and teach game theory as well as millions outside the academy inspired by his remarkable life. Through the academy-award-winning film A Beautiful Mind—the role of Nash famously played by Russell Crowe—viewers experienced Nash’s battle with schizophrenia through his own eyes. The widespread empathy elicited through A Beautiful Mind for sufferers of mental illness helped bring the issue to the forefront of the public agenda.
But many outside academia remain unfamiliar with the earth-shattering contribution of Nash in our ability to model and understand human behavior. Although Nash was a mathematician, it was the social sciences that he revolutionized. And his contribution to the social sciences was truly revolutionary, comparable to that of Louis Pasteur’s breakthrough in germ theory, or to Gregor Mendel’s development of genetics.
As social scientists—economists, political scientists, sociologists, and so forth—we confront a single, intimidating question: how can we make sense of the complexities of human behavior? Prior to Nash, the two mathematicians Von Neumann and Morgenstern had made inroads into developing a formal structure for analyzing human interaction, what is now known as game theory. In the process, they had developed a solution to a special class of games, zero-sum games such as competitive sports, where one player’s loss is the other’s gain. Yet a sense of restlessness prevailed that their work had fallen short. Most human interaction isn’t zero-sum at all; if players can cooperate in some way, they both often benefit. Indeed the very fabric of society rests on the notion that self-interested human beings can gain from different types of cooperative interaction.
Nash’s revolutionary contribution was his development of a solution to virtually every type of game, zero-sum or not. His equilibrium concept, now famously known as the Nash equilibrium, suggested the following: The resolution to any game will be one in which none of the players will choose to change his or her behavior given the behavioral choices of the other players.
This simple solution concept, demonstrated in a sequence of proofs in Nash’s 27-page Princeton doctoral dissertation, laid the foundation for a set of generic games and more advanced solution concepts that can explain behavior and predict outcomes in a wide class of human interactions. Language, measurement systems, currency, migration, fashion, and even political correctness we now understand as “Nash equilibrium” solutions to Coordination games. The intimidation of ISIS toward its Mideast neighbors is a Nash equilibrium in a Hawk-Dove game. Climate-altering pollution levels are a Nash equilibrium in a well-known application of the Prisoner’s Dilemma game, highlighting the obstacles to an international accord on climate change.
What a beautiful mind has left behind is a framework for understanding not only the complexities of human behavior, but the possibility for cooperation even in light of self-interest. It is left for the rest of us to decide how to use gifts like this wisely.