This spring, a record-breaking 248 students enrolled in the Evolutionary Game Theory class taught by Associate Professor of Mathematics Feng Fu. So many students signed up for the course that Fu had to split the class into two sessions to fit into Kemeny Hall’s largest classroom.
Back in 2016, just nine students showed up for the same course.
The meteoric growth in enrollment is just one example of the recent surge of student interest in game theory at Dartmouth. It’s a phenomenon that can be attributed to the subject’s broad applications, and to dynamic faculty like Fu who convey their conviction in game theory’s capacity to help tackle some of today’s seemingly intractable issues.
“We’re facing all kinds of challenges, from pandemics to the ethics of AI,” Fu says. “One way we can find common ground is through evolutionary game theory’s applications, combining mathematical models and social sciences with a mission to change the world for the better.”
A branch of applied mathematics, game theory is a way of modeling and analyzing social situations with competing players, such as price wars in business, coalition building in politics, and survival strategy among animals.
Game theory’s rising popularity at Dartmouth can also be traced to the growth of the Program in Quantitative Social Science, which launched as a major in 2015 and brings together faculty and students interested in applying statistical, computational, and mathematical tools to social science questions.
“When students ask me, ‘Should I take a course in game theory?’ I always say, ‘Yes, this course will change how you think about the world,’” says Michael Herron, the Remsen 1943 Professor of Quantitative Social Science and chair of QSS. “Game theory forces students to think about a social or political situation and look at each of the various actors involved and ask, ‘How is this person responding to others?’”
Cultivating that expanded mindset appealed to Emma Johnson ’24, a double major in theater and QSS.
“We come to Dartmouth seeking answers through education, and we find a subject like game theory that not only offers a toolkit for answering specific social dilemmas but also is applicable to so many different fields,” Johnson says.
Growing interest, broad applications
Pioneered by the polymath John von Neumann in the 1920s, the science of game theory was expanded in the 1950s by Nobel mathematician John Nash, whose life story was adapted into the Hollywood film A Beautiful Mind.
The social sciences have since embraced game theory, especially at Dartmouth. Between Fu’s class and two more courses in Economics and QSS, more than 300 undergraduates study game theory every year.
At the graduate level, there’s a game theory class at Thayer School of Engineering as well as a seminar on game theory this spring taught by Peter Winkler, the William Morrill Professor of Mathematics and Computer Science, among other courses that incorporate game theory into the curriculum.
“For both undergraduates and PhD students, Dartmouth is becoming recognized nationwide as a center for the study of game theory,” Fu says.
Dartmouth first offered an undergraduate course dedicated to game theory in the 1960s through the Department of Mathematics, and in 1993 through the Department of Economics. Two years later, that course was integrated into a course now known as Games and Economic Behavior, which professor Christopher Snyder has taught since 2005.
“There’s some game theory component to any economics story in the news,” says Snyder, the Joel Z. and Susan Hyatt Professor of Economics, noting the subject’s applications to labor, macroeconomics, finance, international trade, industrial organization, and even pharmaceutical drug development.
For example, in Snyder’s 2021 article Market Design to Accelerate COVID-19 Vaccine Supply, published in Science, he and his coauthors found that the economic benefit for a person receiving a COVID-19 vaccine was approximately $5,800, even while vaccine producers were only getting paid $6 to $40 per vaccine course, “indicating the wide gap between social and commercial incentives.”
Using principles from game theory, Snyder suggested policies that might incentivize vaccine producers to bridge the gap.
Snyder has seen steady demand of 60 to 70 undergraduates a year for the class, with a number of students embracing the subject in their careers. One of Snyder’s earliest students was Owen Zidar ’08, who later credited the course with setting him on the path to a PhD in economics at Berkeley and a professorship at Princeton University.
Another former student, Ran Zhuo ’17, wrote a senior thesis under the supervision of Snyder and professor Doug Staiger, which was accepted for publication in the Journal of Industrial Economics before she graduated. She went on to a PhD program in economics at Harvard and will join the University of Michigan this spring as an assistant professor.
The first sign of a real spike in student interest in game theory was in 2020, when enrollment in Herron’s Introduction to Game Theory surged to 90—three times above the average that he had seen since offering the course in 2004. Herron credits some of the interest to what was then the relatively new QSS major, which evolved from a program known previously as Mathematics and Social Sciences.
Whereas MSS had one to two majors a year, QSS now has 50 to 60 active majors, Herron says, and they’re all required to take a game theory course.
In the QSS Introduction to Game Theory course, students get familiar with concepts such as the prisoner’s dilemma, a situation where two players acting selfishly undermine their optimal self-interest. Understanding where and why this happens—be it in law enforcement, sports games, or international trade—can help policymakers devise ways of creating more socially advantageous results for everyone.
Outside the classroom, Herron draws on game theory in his own research to analyze voter behavior, gun violence, and other collective action problems. In an article for Rationality and Society that Herron co-authored with former student Zachary Markovich ’15, the two utilized game theory to analyze grade inflation and offer solutions. (Markovich is now a PhD candidate in political science at MIT.)
Along with teaching core concepts such as equilibrium, which is a way of conceptualizing homeostasis among competing players and predicting behavior, Snyder also reserves class time for the lighter side of game theory. For one class period, for example, he hosts a rock-paper-scissors tournament with a $30 prize, simulating a professional lab experiment with incentivized players.
“It’s probably one of the few classes at Dartmouth where the students get paid by the professor,” Snyder says. “I literally pull cash out of my pocket.”
Liberal Arts for the 21st century
Dan Rockmore, the William H. Neukom 1964 Distinguished Professor of Computational Science (and member of the QSS steering committee), sees Dartmouth’s strength in game theory as an “evolution of the liberal arts for the 21st century.”
“Students with all kinds of nonSTEM-centric interests seem increasingly interested in learning about the ways in which data and technology help to build out a broad education and understanding of the world and give another language and approach for the kinds of critical thinking that we hope to inculcate here at Dartmouth,” Rockmore says.
“Although Professor Fu’s class is listed as a mathematics course, it’s not all about the math,” says Kevin Hu ’20, a QSS major who took Fu’s class in 2018. “More valuable than developing familiarity with mathematical formalisms of specific game theory models are the intuitions and mental models about decisionmaking that students can leave the class with.”
Hu completed a QSS honors thesis with Fu on understanding gig labor preferences through the lens of evolutionary game theory, which was subsequently published in the journal Games.
Phoebe Ford ’23 said Fu’s course, which counted as an elective toward her computer science major, caught her eye because it focused more on problem-solving applications and less on coding and mechanics. While a calculus background is required, no coding knowledge is necessary, which has surely helped widen the class’s appeal.
“Fu is known for his lively and exciting lectures,” says Ford, who took the class last spring. “From penalty kicks to rock-paper-scissors, we learned that the implementation of mathematical strategies can increase the success rate for events you may think are based on luck. You hear about game theory, and it sounds like an abstract concept, but this course taught me the practicality of math application to decisionmaking and evolution.”
Fu concludes Evolutionary Game Theory with each student group delivering TED-style presentations on a topic of their choice. Past projects have applied game theory to analyses of fake news on social networks, recycling practices, and the hypothetical legalization of a government-regulated market for organ transplants.
“The breadth of topics really highlighted how evolutionary game theory could be applied broadly across domains,” says Hu, who is now a graduate student in data science at the University of Oxford.
For Rockmore, Dartmouth’s strength in game theory advances a theme that renowned professor and computer scientist John Kemeny, who later served as Dartmouth president, started on campus nearly 60 years ago when he co-developed the BASIC programming language.
“He believed that an understanding of computing was foundational to the liberal arts and a Dartmouth education,” Rockmore says. “With their engagement with quantitative social science and game theory, students today seem to have come to the same conclusion.”