New York University political scientist Steven Brams wants to help Hamlet revamp his image. Readers of Shakespeare’s play remember the eponymous prince of Denmark mostly for his waffling—“To be, or not to be, that is the question”—and therefore tend to regard him as indecisive.
Not so, Brams told the crowd that packed the MAA Carriage House on November 14 for his contribution to the Distinguished Lecture series. “Hamlet was a completely strategic character.” Hamlet bided his time not because of a flawed and hesitant nature, Brams argued, but because he needed to gather more information about Claudius’s role in his father’s death.
And Brams’s lecture provoked reevaluation of more than just Prince Hamlet’s certitude. As he surveyed examples analyzed in more detail in his 2011 book Game Theory and the Humanities: Bridging Two Worlds, Brams treated his audience to new perspectives on Lysistrata and Catch-22, the Civil War and the 1979 Iran hostage crisis.
Before comparing the Cuban missile crisis to a game of chicken, though, or revealing the land grabs that motivated many a medieval witch trial, Brams situated his work in the history of game theory. He traced its origins to a 1944 book by John von Neumann and Oskar Morgenstern, Theory of Games and Economic Behavior.
Though the mathematically dense tome did “not exactly take the world by storm,” Brams quipped, the ideas contained therein did get out. By the 1950s strategists were using game theoretic methods to better understand arms races and nuclear deterrence. Economists became interested in the 1960s and '70s, Brams said, and political scientists got in on the fun in the '70s and '80s. Currently, evolutionary biology relies on game theoretic models, and enterprising academics like Brams are applying game theory beyond the social and natural sciences, in fields from literature and history to philosophy and even law.
“Game theory is powerful in highlighting the main strategic lines of thinking of the players and why they make the choices that they do,” Brams said.
Brams, though, has changed the rules of standard game theory, introducing what he calls the “theory of moves.” Players in Brams’s games don’t just think rationally, they think ahead. They consider not only what move they’re inclined to make in the present, but what actions and counteractions that move is likely to precipitate.
When Brams analyzes a game, he looks to find not the Nash equilibrium (though he identifies that, too), but the “nonmyopic equilibrium,” the stable solution that will result if the players bring to the interaction both rationality and foresight. Which equilibrium is reached depends on the status quo, the state of affairs when the game begins.
Brams considers nonmyopic thinking “characteristic of humans,” and he believes it ought to be incorporated into behavioral analyses.
So...want insight into why the Confederacy, knowing it had inferior resources, went to war with the United States? Curious about the ebb and flow of religiosity over the ages?
Brams admits that it’s impossible to capture the complexities of the Civil War in a two-by-two matrix, but he does use this tool of game theory (among others, of course) to demystify human actions, be they fictional or historical.
Watch a slidecast of his lecture (available soon) to learn more. —Katharine Merow
Read an interview with Steven Brams that appeared in the September 2010 issue of the College Mathematics Journal (pdf)
This MAA Distinguished Lecture was funded by the National Security Agency.