Economist Larry Samuelson on Pioneering Game Theory Research at Cowles

By Richard Panek

The question came about two-thirds of the way through a seminar at the London School of Economics in the 1980s. Larry Samuelson, then an early-career economist, was giving a talk on the topic of bargaining when a hand shot up.

Why, the audience member wanted to know, do we even need game theory?

“You wouldn’t get that question today,” says Samuelson, now the A. Douglas Melamed Professor of Economics at Yale University and a member of the Cowles Foundation for Research in Economics. And the reason you wouldn’t get that question today is that Samuelson’s generation of economists has made sure you wouldn’t. They’ve taken the once-peripheral field of game theory and, over the course of four decades, made it not only mainstream among economists but inextricable from economics itself.

A Sensation Among Professional Economists

Game theory in economics dates only to the 1944 publication of mathematician John von Neumann and economist Oskar Morgenstern’s Theory of Games and Economic Behavior. The book was itself an elaboration on a 1928 paper by von Neumann offering a mathematical proof for the minimax theorem, which traces how two players in a zero-sum game can arrive at strategies that, even though one player will inevitably win and the other will inevitably lose, will maximize both of their payoffs.

Before von Neumann, economists had focused on models for competitive markets—the kind in which a consumer assumes that an individual decision whether or not to purchase a can of beans will have no effect on the price of a can of beans. In competitive markets, the economists’ focus is on a straightforward question: What action provides the most advantageous outcome for me?

Theory of Games, however, offered an alternative interpretation of human action: human interaction. The question remained the same, but with a difference: What action might provide the most advantageous outcome for me…if I take into account the possible actions of others? Von Neumann and Morgenstern didn’t focus on the actions of anonymous actors in competitive markets, the traditional province of economic analysis. Instead, they focused on strategy—especially in the creation of mutually beneficial coalitions.

Finding the math to capture on paper that shift in perspective—from passive participation to active strategizing—would require new analytical tools, which Theory of Games began to provide. The book, though, was dense, and mathematicians, economists, and researchers in other fields needed a year or so to recognize its significance. But when they did, the book’s impact proved so extensive that, on March 10, 1946, the New York Times featured the phenomenon on the front page.

“A new approach to economic analysis that seeks to solve hitherto insoluble problems of business strategy,” read the opening of the article, “has caused a sensation among professional economists.”

And beyond, as the article emphasized: beyond professional economists, beyond the marketplace. The article quoted from an essay in The American Economic Review by Leonid Hurwicz, an economist associated with the Cowles Commission for Research in Economics (then affiliated with the University of Chicago and a forerunner of the Cowles Foundation at Yale): “It would be doing the authors an injustice to say that theirs is a contribution to economics only. The scope of the book is much broader. The techniques applied by the authors in tackling economic problems are of sufficient generality to be valid in political science, sociology, or even military strategy.”

The mention of military strategy was prophetic. In 1950 mathematicians Merrill Flood and Melvin Dresher, consultants to the RAND Corporation, tried to game out nuclear proliferation in the nascent Cold War. They arrived at a model showing that two adversaries, working with no knowledge of the other’s strategies or actions but needing to make an educated guess, faced overwhelming incentives that were individually advantageous yet mutually disastrous.

The young mathematician John Nash soon realized that if the two sides played the game over and over, they would adopt more elaborate strategies allowing them to use current play to reward, punish, or teach opponents about past play. By moving beyond zero-sum games, Nash established the possibility of opponents reaching equilibrium cooperation. The Cold War eventually reached its own “Nash equilibrium”: Mutually Assured Destruction.

Although Flood and Dresher’s work for RAND arose independently of economics, analogous situations in the field clearly abounded. For instance, two or more manufacturers of an identical product would, in the abstract, benefit most by cooperating from the start: Acknowledge their similarities, set high prices, then divvy up the market and the profits. But in game theory, as in human nature, reciprocal trust is rare, and so the manufacturers wind up trying to out-compete one another—for instance, through ruinous price competition and advertising.

Viewers of Mad Men might remember the scene in the series pilot in which advertising executive Don Draper tries to win the account of a tobacco behemoth in the wake of a Reader’s Digest article linking cigarettes with cancer. “We have six identical companies making six identical products,” he says. “We can say anything we want”—just as long as prospective customers feel good about themselves.

He turns to the blackboard in the conference room and scratches out the slogan that he wants the client to consider: “It’s toasted.”

“But everybody else’s tobacco is toasted,” says the scion of the tobacco empire.

“No,” Draper says. “Everybody else’s tobacco is poisonous. Lucky Strike’s”—two knuckle raps on the blackboard—“is toasted.”

Incomplete Information

Larry Samuelson was born in 1953 in Rockford, Illinois, then a solidly blue-collar, middle-class, Midwest industrial town. After high school Samuelson decided to go away to college—the University of Illinois at Champaign-Urbana (today, Urbana-Champaign), a three-hour drive from Rockford—although he had "not much of an idea” about what he wanted to study. Instead, he had chosen to attend college because, on the scale of good-for-me/bad-for-me, he guessed it would be more advantageous than the alternative.

His willingness to take the road less traveled resurfaced when the time came to choose classes. He happened upon an economics course and, without knowing why, signed up. The course proved to be revelatory. The teacher was “particularly inspiring,” Samuelson says, but it was the subject itself that riveted him.

He already knew that he liked mathematics—its “logic,” he says, its “beauty.” But in economics he discovered “an ideal blend of precision and rigor on the one hand, and relevance on the other hand.” After graduation he stayed at the University of Illinois to pursue a masters in economics and then a doctorate. “Being an economist,” he says, explaining the reasoning behind his choice of career, “you’re doing math in the service of what looked like some really important questions.”

In the mid-1970s game theory wasn’t part of the standard curriculum in the study of economics; it was what Samuelson calls “a specialty.” Nonetheless, Illinois did offer a course on the topic, and as a graduate student Samuelson, once again electing for an option off the beaten path, took the course—and, once again, found a fortunate combination of inspiring instructor and compelling topic. One of the teachers in that class was Alvin E. Roth, future co-recipient, with Lloyd Shapley, of the Nobel Prize in Economic Sciences partly for his work on, yes, game theory.

Samuelson also opted for another out-of-the-box class, this time on the subject of incomplete information—a form of game theory in which participants don’t possess full information about their opponents. He continued to pursue that topic after receiving his doctorate, and in fact incomplete information would be the topic of the London School of Economics seminar that Samuelson was leading in the early 1980s when he called on an attendee who asked the questions that crystallized for Samuelson a before-and-after moment in modern economics:

Why can’t the sides in a negotiation just write a contract, a pact, an agreement—a something that covers everything? Why do we need all this game theory apparatus anyway?

The Life of an Itinerant Academic

Economics in the 1980s was ripe for a revolution.

By the end of the 1950s economists, most prominently Kenneth Arrow and Gérard Debreu (both longtime associates of the Cowles Commission in Chicago and the Cowles Foundation at Yale), had found and solved a mathematical model for economic equilibrium in the competitive market—the one in which actors make independent decisions, and the market adjusts supply and demand accordingly. Samuelson calls that late-1950s model of equilibrium “the capstone of the theory of competitive markets.” It was, he says, a “story” compelling enough to suffice for the next twenty years.

By the 1980s, though, some economists were beginning to wonder if it was the whole story. After all, the theory depended on what Samuelson calls “inapplicable approximations of many real-world settings”: “No trading frictions. No barriers to interaction. Perfect information.” The theory of competitive markets worked (in theory), but it was inadequate for the questions that were increasingly interesting economists, including market power, market failure, market design, and incomplete information. Those questions, Samuelson says, “are naturally approached with game theory.”

The time had come for those interactive, strategizing players that von Neumann and Morgenstern had introduced in Theory of Games to migrate from the periphery of Samuelson’s field to the mainstream. The basic tool for doing so would be the concept of a Nash equilibrium. Before long game theory was part of the curriculum of just about every graduate program in economics.

After completing his PhD in economics at Illinois, Samuelson embarked on the life of an itinerant academic. For a year he taught at the University of Florida, Gainesville, then for three years at Syracuse University, then for the rest of the 1980s at Pennsylvania State University. In 1990 he settled down at the University of Wisconsin, Madison, and there he remained for nearly two decades, before joining the faculty at Yale in 2007. Along the way Samuelson became a leading figure in two subsets of game theory in economics.

One was evolutionary game theory.

At first, the evolution in evolutionary game theory was metaphorical. From the late 1980s through the 1990s, Samuelson studied scenarios in which players would adjust their behavior over the course of repeated plays of a single game, experimenting with various actions and gravitating toward those that had tended to bring good outcomes and away from actions that had produced disappointing results. The basic question was whether such learning would lead players in a game to a Nash equilibrium, and the basic answer, albeit with many caveats and qualifications, was yes: Stable outcomes of learning dynamics are Nash equilibria.

Then Samuelson began taking the word evolution more literally, extending his mathematical work on evolutionary game theory into biology. In collaboration with Yale evolutionary biologist and ornithologist Richard Prum, for instance, Samuelson studied cases of members of a species mimicking the members of other, typically more dominant, species. The example they used in a 2012 paper was the evolution of Downy Woodpeckers that are now nearly identical in appearance to the generally larger Hairy Woodpeckers.

Mimicry is common in the natural world. The standard explanation for its existence has been that it emerges when two or more species converge in appearance or on some other characteristic in order to more effectively convey information, such as their own toxicity, to a third, perhaps predatory, species. In contrast, Samuelson and Prum interpreted Downy and Hairy Woodpeckers as an example of “interspecific social dominance mimicry.” If Downy Woodpeckers, averaging six inches in height, hadn’t engaged in evolutionary mimicry to resemble the more dominant Hairy Woodpeckers, averaging nine inches in height, they would have to surrender whenever contesting a resource.

But Hairies themselves fall into two categories. Some are passive: “doves,” in ornithological terminology. Some are aggressive: “hawks.” The hawks dominate the doves (while also trying to dominate their fellow hawks—but that’s another evolutionary story), leaving the doves to divide the remaining resources among themselves. Which they do, amicably.

Enter—literally—the Downies. Despite their smaller stature, Downies can mingle among Hairies because their plumage has evolved to almost perfectly mimic the black-and-white patterns of the more dominant species. A close physical resemblance alone, however, might not provide the crucial evolutionary component. Downies also benefit from the tendency among Hairy doves to back down from confrontation without investigating their opponents too closely. If Samuelson and Prum are right, then mimicry has allowed Downies to have access to resources that would otherwise be unavailable to their own species. And subsequent field work has in fact begun to validate Prum and Samuelson’s interpretations of how mimicry operates in the wild.

More recently, Samuelson has extended his literal interpretation of the word evolution. Rather than using evolution to study other species, he has begun applying it to the biology of humans.  An old joke: The reason economists don’t sell their children is that they might be worth more later. And yes, Samuelson grants, “the mechanics of evolutionary selection are fundamentally selfish. Evolution selects for traits, behaviors, and preferences that increase the reproduction prospects of the individual, or indeed more precisely the gene.”

But.

“There's nothing intrinsic to economics that requires people to be selfish,” Samuelson says. Economic theory assumes that behaviors follow preferences, but it makes no assumptions about the content, whether selfish or selfless, of those preferences. “To an economist Mother Teresa is as good a model of economic behavior as is”—a pause—“Elon Musk might come to mind. Mother Teresa was as selfless as could be, but she followed that goal consistently and coherently, and one would have no trouble fitting that into an economic model.”

And because preferences “are the point of departure for models of individual behavior,” they are also the point of departure “for all of economics.” Biological and cultural evolution helped shape our preferences just as it helped shape many of our characteristics. By identifying aspects of preferences that would have conferred an advantage on our evolutionary ancestors, Samuelson’s research has allowed economists to sharpen their assumptions about preferences and therefore the subsequent economic analyses.  

In the late 1990s Samuelson began investigating the topic that would become his second major area of research: repeated games, especially the concept of reputations. As the name suggests, repeated games involve modeling that extends beyond the decision-making apparatuses of a one-off competition.

The key question in a repeated game, as it was in the aftermath of von Neumann and Morgenstern’s Theory of Games, is still: What action might provide the most advantageous outcome for me if I take into account the possible actions of others?  In the case of a repeated game, players often have an opportunity and an incentive to build reputations for acting in a certain way, in order to influence the actions of others. “If you and I interact repeatedly,” Samuelson says, summarizing the pre-existing literature on the subject, “then we can have incentives to do things that we wouldn’t if we interacted just once.”

Samuelson, however, studied situations in which reputations might be either impossible to establish or impossible to maintain indefinitely. One major finding of his was that situations can exist in which a player is unable to establish a reputation for competence because attempts to do so would paradoxically work too well. A customer of a firm with such a sterling reputation might be forgiving of a bad experience, attributing it to unfortunate luck rather than a failing of the firm. But then, Samuelson says:

“The firm has a license to provide low quality or poor service without damage to its reputation, causing the reputation to unravel—and ensuring that the firm cannot build the reputation in the first place. It can thus be good for a firm to have its customers think that there is always the chance that something has gone wrong at the firm, causing it to no longer be capable of providing high quality or good service.  Any poor experiences are then attributed to the actions of the firm rather than bad luck, ensuring that every misstep threatens the firm’s reputation, and hence creating the continuing incentives to provide high quality or good service that allows the firm to build a reputation in the first place.”

Incentives Matter

By the 2010s Samuelson had become somewhat of an elder statesmen in the field of game theory economics. In 2011 he was elected to the American Academy of Arts and Sciences. The following year he received a fellowship from the Society for the Advancement of Economic Theory. From 2014 to 2020 he served as the director of the Cowles Foundation, where he initiated a homecoming of sorts: In 1934 Alfred Cowles, champion of the use of statistics in economics, helped fund the launch of the Econometrics Society, and Samuelson, in his role at the head of the Cowles Foundation, orchestrated the transfer of the Society’s office to Yale. As of 2025 Samuelson is serving as the president of the Society.

Not surprisingly his five-decade immersion in game theory has affected his view of the world. “I think about incentives a lot,” he says. “If I had to summarize all of economics in one phrase, that phrase would be: Incentives matter. That sounds trite,” he quickly adds, “but it’s something people very easily lose sight of.”

So what, I wonder, was his incentive to sit for this interview? What went through his game theorist’s brain when the current director of the Cowles Foundation invited him to be the subject of the first of what might become a series of faculty profiles on the Cowles website? Can Samuelson describe his decision in terms of game theory?

He immediately defaults to a familiar framing.

“This could be good for the organization, and indirectly that’s good for me. Or,” he goes on, after a moment’s reflection, “at least it makes me feel good about me.”

In short: It was toasted.