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For his brilliant insight into human behavior
For his brilliant insight into human behavior
For his brilliant insight into human behavior
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For his brilliant insight into human behavior
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Sold in part to Benefit the John C.M. Nash Trust
For his brilliant insight into human behavior

JOHN FORBES NASH, JR., 1994

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For his brilliant insight into human behavior
John Forbes Nash, Jr., 1994
The 1994 Nobel Prize in Economic Sciences awarded to John Forbes Nash, Jr. for his contributions to Game Theory, namely introducing the "distinction between cooperative games, in which binding agreements can be made, and non-cooperative games, where binding agreements are not feasible. Nash developed an equilibrium concept for non-cooperative games that later came to be called Nash equilibrium."

NASH, JR., John Forbes (1928-2015). The Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel awarded to John Forbes Nash, Jr. in 1994. 18 carat gold, 65mm diameter, 180.6 grams. Profile of Alfred Nobel facing left on obverse, with "Sveriges Riksbank till Alfred Nobels Minne 1968" (The Sveriges Riksbank, in memory of Alfred Nobel, 1968) around the upper side and the bank’s crossed horns of plenty below, reverse with the North Star emblem of the Royal Swedish Academy of Sciences, dating from 1815, with the words “Kungliga Vetenskaps Akademien” (The Royal Swedish Academy of Sciences). "J.F. Nash" engraved on the edge of medal. Housed in original red morocco gilt case, lettered "J.F. Nash," interior lined with velvet and satin. WITH: John Forbes Nash, Jr.'s 1994 Nobel Prize Diploma, two leaves, 330 x 207mm, in tan morocco gilt portfolio and original suede-lined blue cloth clamshell box; both portfolio and box gilt-lettered with recipient’s initials on upper covers; housed in original velvet pouch.

25 years ago, on 11 October 1994, The Royal Swedish Academy of Sciences decided to award the Bank of Sweden Prize in Economic Sciences in Memory of Alfred Nobel jointly to Dr. John F. Nash, Princeton University; Professor Dr. Reinhard Selten, Rheinische Friedrich-Wilhelms-Universität, Bonn, Germany; and Professor John C. Harsanyi, University of California, Berkeley, for their pioneering analysis of equilibria in the theory of non-cooperative games.

A brilliant insight into human behavior

The contributions to economics that garnered John Forbes Nash, Jr., a Nobel prize in 1994 began to surface around 1949, when he was all of 21 years old. What was perhaps the chief insight—the Nash equilibrium—came on the heels of several weeks crammed with exams, where the break from research had given vague ideas the chance to take shape.

As a student at Princeton, Nash was spending his summers at RAND, the civilian think tank in Santa Monica. RAND was one of the first think tanks to focus on nuclear strategy, which in 1950 was a source of anxiety worldwide. Military strategists were the first to see the value in game theory and they sought to apply it to nuclear defense, from intelligence missions to bombing patterns. Where game theory had previously focused on two-person zero-sum games—e.g., win-lose scenarios that inflict the greatest amount of damage on an enemy—researchers were beginning to realize this view held limited applicability to the real world.

Enter John Forbes Nash, Jr. He broadened the view from two-person zero-sum games, and provided a tremendously valuable mathematical framework within which to analyze conflict. He introduced the distinction between cooperative and noncooperative games, and demonstrated that in multi-player interactions, each player always has a dominant strategy that is a best response to other player's strategies. It was simple, it was brilliant, and it would provide a general unifying structure for analyzing social institutions of all kinds.

It was a breakthrough that has been compared to those of Newton and Darwin. Fellow Laureate Roger Myerson would call it "one of the great watershed breakthroughs in the history of social science," noting that "Nash's theory of noncooperative games should now be recognized as one of the outstanding intellectual advances of the twentieth century. The formulation of Nash equilibrium has had a fundamental and pervasive impact in economics and social sciences which is comparable to that of the (nearly contemporaneous) discovery of the DNA double helix in the biological sciences." Biographer Sylvia Nasar would call it a "brilliant insight into human behavior." Mathematician and economist David Gale reflected later, "He had a concept that generalized to disarmament," and Nash's own co-recipient Reinhard Selten would observe: "Nobody would have foretold the great impact of the Nash equilibrium on economics and social science in general" (qtd in Nasar, pp.93-98).

Nash would close his biographical essay for the Nobel Prize with this observation: "Statistically, it would seem improbable that any mathematician or scientist, at the age of 66, would be able through continued research efforts, to add much to his or her previous achievements. However I am still making the effort and it is conceivable that with the gap period of about 25 years of partially deluded thinking providing a sort of vacation my situation may be atypical. Thus I have hopes of being able to achieve something of value through my current studies or with any new ideas that come in the future." Nash would keep working and achieving for the next twenty years. He received the prestigious Abel Prize just before his death in 2015.

The Nobel Prize and diploma are together with the following items relating to the ceremony: Typed letter signed, 11 October 1994, from the Royal Swedish Academy of Sciences, notifying Nash of his award; Nash's copy of Les Prix Nobel 1994, Stockholm: Nobel Foundation, 1995; Nash's handwritten dimensions for his formal attire, signed ("John Forbes Nash"), one page, c.October 1994; and Nash's nametag ("Dr. John F. Nash, Economics") bearing the Nobel logo.
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GOLD MEDALS FOR GAMES

Game theory is the science of strategy. In most political, social, and economic interactions, the choices of the participants impact one another. Therefore each has to think about others’ decisions, recognizing that conversely the others are thinking about theirs. Amazingly, this complex thinking about thinking can be systematized. Research on how to do so has led to several Nobel prizes, starting with those to John Nash, Reinhard Selten, and John Harsanyi 25 years ago in 1994.

People have been making strategic decisions for millennia, perhaps most dramatically in military conflicts, but also in dealing with family, friends, business rivals, and sports opponents. They have developed a lot of art specific to their experiences. Game theory builds on that, identifies common features, and develops general principles which can then facilitate strategic thinking for new applications.

The first such successful theorizing came from the polymath John von Neumann and his economist coauthor Oskar Morgenstern. They considered two-person games of pure conflict (win-lose or zero-sum games) where one player’s gain necessarily entails the other’s loss. Sports contests are the best-known examples. Von Neumann and Morgenstern proved a mathematical theorem: that zero-sum games always have an equilibrium, a pair of strategies, one for each player, such that neither can gain by deviating to a different strategy. They also showed that the equilibrium often involves mixing moves: acting randomly on any one occasion so as to keep the other player guessing. For example, a penalty kicker in soccer should not always kick to the goalie’s left. The theorem also shows how to calculate the proportions in which the kicker should mix left and right kicks.

But most games have more than two players, and can be win-win (international trade) or lose-lose (nuclear arms race). Most games are not one-offs; they can be repeated, or be a part of a sequence of different interactions. Advances in game theory have enabled us to understand such games and their outcomes.

JOHN NASH

John Nash’s first Nobel-worthy contribution proved that many-player, non-zero-sum games also have an equilibrium: a configuration of all players’ strategies where no one has any incentive to switch to a different strategy. With Nash equilibrium in hand as their “solution concept” for understanding and predicting strategic behavior, social scientists could now investigate countless applications that had previously eluded systematic investigation, in fields from economics and law to political science and military strategy, even biology.

As fellow Nobel Laureate Roger Myerson put it in his own homage: “Nash carried social science into a new world where a unified analytical structure can be found for studying all situations of conflict and cooperation…The formulation of Nash equilibrium has had a fundamental and pervasive impact in economics and the social sciences, comparable to that of the discovery of the DNA double helix in the biological sciences.”

The best-known example of Nash equilibrium in action is the Prisoners’ Dilemma. Nash’s Ph.D. adviser Albert Tucker invented the story of this game. The police interrogate two suspects separately, and suggest to each that he or she should fink on the other and turn state’s evidence. “If the other does not fink, then you can cut a good deal for yourself by giving evidence against the other; if the other finks and you hold out, the court will treat you especially harshly. Thus no matter what the other does, it is better for you to fink than not to fink—finking is your uniformly best or ‘dominant’ strategy.” This is the case whether the two are actually guilty, as in some episodes of Law and Order, or innocent, as in LA Confidential. Of course, when both fink, both fare worse than if both had held out. Although holding out is jointly better, it does not survive their separate temptations to fink—it is not a Nash equilibrium!

These dilemmas arise everywhere. Perhaps the biggest concerns action to combat climate change. Each country wants to continue its economic growth, but more economic activity usually requires more greenhouse gas emissions. Any one country’s emissions add only a little to the total accumulation of these gases. But when all countries give in to the temptation to pursue growth, the effect is substantial and the resulting warming puts humanity’s future at risk.

Such dilemmas can be resolved in multiple ways. First, if players interact repeatedly over a long time horizon, then fear of lost future cooperation may keep them cooperating today; this is the well-known tit-for-tat strategy. Second, a “large” player who suffers disproportionately more from complete finking may act cooperatively, tolerating small-fry finking. Thus the United States bears a disproportionate share of the costs of its military alliances. Finally, if the group as a whole will do better in its external relations if it enjoys internal cooperation, then biological instincts or social norms that support cooperation and punish cheating can arise and prevail. Many biologists claim that the evolution of cooperation in humans has such game-theoretic origin. In fact, any “evolutionarily stable” outcome of an evolving biological system corresponds to a Nash equilibrium of an “evolutionary game.”

Nash’s formulation of the concept of “Nash equilibrium” and proof of equilibrium existence would have been enough. But he had a second contribution worthy in its own right of a Nobel prize: a theory of bargaining known as “Nash bargaining” that is the mainstay of most subsequent theories and applications to labor-management negotiations, international trade, and merger analysis, among other areas.

REINHARD SELTEN

Unlike Nash, whose star immediately shone, Reinhard Selten’s seminal work languished nearly unknown at first. Indeed, it was not until 1980 that Selten’s earliest Nobel-cited work (published in 1965 in Staatswissenschaft) was mentioned in an English-language review. But then the floodgates opened dramatically. In 1982, five brilliant young theorists—Ariel Rubenstein on bargaining; David Kreps and Robert Wilson on reputation; and Paul Milgrom and John Roberts on entry deterrence—all built on Selten’s foundation with seminal contributions that may, one day soon, win their own Nobel prizes.

Selten’s contributions, most notably, “subgame perfection,” refine Nash’s concept: in some situations, many sorts of outcomes can be consistent with equilibrium, making it difficult to gain insight into the economic phenomena being studied. However, Selten showed that Nash equilibria can be refined down to a smaller set, by discarding information that fails to pass certain plausibility tests (e.g., by disallowing Nash equilibria in which any player makes a non-credible threat which, if put to the test, she would back away from carrying out).

Together, John Nash and Reinhard Selten laid the groundwork for a blossoming of the social sciences that continues to this day. The discoveries honored by these Nobel Prizes changed the game of how we understand and compete in our ever-changing world. We hope that whoever secures these treasures finds a way to share them with the world, to inform and inspire future generations.

- Avinash Dixit, David McAdams, and Susan Skeath

Avinash Dixit is University Professor of Economics, Emeritus, at Princeton and the author of Art of Strategy (with Barry Nalebuff; W.W. Norton, 2008). David McAdams is Professor of Economics at Duke University and the author of Game-Changer (W.W. Norton, 2014). Susan Skeath is Professor of Economics at Wellesley College and Acting Director of the Quantitative Reasoning Program. Together they are coauthors of the forthcoming fifth edition of Games of Strategy (W.W. Norton, 2020).

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