**John Nash was one of the pioneers of game theory and in 1994 was awarded the Nobel prize in economics for his work in this field. He was also the subject of the 2001 film, A beautiful mind, where the young John Nash was played by Russell Crowe, for which he won an Oscar.**

Tragically, John Nash and his wife were killed in a car crash on May 23: he was 86 years old. Since his death there have been many tributes paid to him and his work.

As a student of economics you will almost certainly have studied the concept of a Nash equilibrium: a situation where everyone makes their best choice, given the choices of the other ‘players’ in a ‘game’. But a Nash equilibrium is not in the collective best interests of the participants in a non-cooperative game.

This is a very different concept of equilibrium from the simple equilibrium in a perfectly competitive market. In fact, in the complex world of strategic decision making, where firms are constantly looking at their rivals’ behaviour and possible reactions to their own behaviour, there are all sorts of Nash equilibria which are clearly sub-optimal. Competition may be highly destructive.

The following obituaries look at Nash’s contribution to the development of economics. As the Bloomberg article states:

The game theory concepts that Nash’s math[s] brought to the field were a true paradigm shift in economics. Macroeconomists, who continue to use the old Walrasian notion of equilibrium typically engage in hand-waving about how the macroeconomy is too big for strategic interactions to matter. But most of the economics profession has gradually shifted toward Nash equilibrium. The 2014 Nobel winner, Jean Tirole, is emblematic of the new economics. And many of the biggest successes in applied economics, like the auctions that power Google’s advertising, rely on Nash’s technique.

Do we owe him as much as Adam Smith?

### Articles

Death of John Nash and His Beautiful Ideas *Bloomberg*, Noah Smith (26/5/15)

John Nash, economist and mathematician, 1928–2015 *Financial Times*, Ferdinando Giugliano (25/5/15)

Obituary: John Nash: Lost and found *The Economist* (28/5/15)

Remembering John Nash: Finding equations to explain the world *The Economist* (28/5/15)

John F. Nash Jr., Math Genius Defined by a ‘Beautiful Mind,’ Dies at 86 *New York Times*, Erica Goode (24/5/15)

Explaining a Cornerstone of Game Theory: John Nash’s Equilibrium *New York Times*, Kenneth Chang (24/5/15)

John Nash’s Indelible Contribution To Economic Analysis *Forbes*, Jon Hartley (25/5/15)

John Nash’s ground-breaking contributions to maths *BBC News*, John Moriarty (24/5/15)

From the archives: Nash’s Nobel prize *The Economist* (24/5/15)

A beautiful strategy: John Nash’s ‘game theory’ explained *Hindustan Times*, Gaurav Choudhury (25/5/15)

### Interview with John Nash

Interview with John Nash *Nobelprize.org* (Sept 2004)

### Questions

- What is meant by the ‘prisoners’ dilemma’? How is this a demonstration of a sub-optimal Nash equilibrium in a non-cooperative game?
- Why is it difficult to predict the outcome of a non-cooperative game?
- Give some examples of non-cooperative games played by companies competing with each other.
- Give some examples of non-cooperative games played by nations competing with each other.
- Why do competition authorities try to prevent cooperation between businesses?
- Why may a cooperative equilibrium between firms be an unstable one?