John F. Nash Jr (b. 1928)

John Forbes Nash was born in Bluefield, West Virginia, USA in 1928. Both his parents were graduates and they took an active interest in their son’s intellectual development. Nash was something of an independent learner and in his early teenage years he was conducting scientific experiments and solving challenging mathematical problems on his own. In 1945 he joined the Carnegie Institute of Technology (now Carnegie-Mellon University) having won a scholarship in the George Westinghouse Competition. He began by studying chemical engineering before switching to chemistry and then mathematics. Because of the notable progress Nash then made, when he graduated in 1948 he was awarded both a BS and an MS. Nash credits this achievement to extra mathematics schooling his parents had arranged for him while he was still in Bluefield. Carnegie also gave him his first brush with economics – an elective he took in international economics that was to lead to both his Econometrica paper ‘The Bargaining Problem’ (Nash, 1950c), and his interest in game theory (Nobel Foundation, 2004).

On the strength of a remarkable recommendation from Carnegie – it read simply ‘This man is a genius’ – Nash was offered graduate student fellowships by Princeton and Harvard universities (Kuhn et al., 1996). It has been suggested that his preference was for Harvard, but Princeton offered him more generous terms and seemed keener to attract him; Nash opted for Princeton. His PhD thesis (Nash, 1950a), containing the work that would win him the Nobel Prize, was accepted by Princeton’s Mathematics Department in 1950. Nash was 21.

After completing his PhD, Nash stayed at Princeton for a year as an instructor before moving to the Massachusetts Institute of Technology (MIT) as C.L.E. Moore Instructor. For a time he also worked for the RAND Corporation. In 1956–57 he returned to visit Princeton on a sabbatical funded by an Alfred P. Sloan award. Nash remained at MIT until resigning in 1959 because of mental health problems with which he struggled for a long time. He is currently senior research mathematician in the Department of Mathematics at Princeton.

Nash’s honours include the award (jointly with Carlton E. Lemke) in 1978 of the John von Neumann Theory Prize by the Operations Research Society of America and the Institute of Management Sciences. In 1999 he received the Leroy P. Steele Prize from the American Mathematical Society. In 1994 Nash was awarded the Nobel Memorial Prize in Economics, together with John Harsanyi and Reinhard Selten, ‘for their pioneering analysis of equilibria in the theory of non-cooperative games’ (Nobel Foundation, 2004).

Nash’s work has been pivotal in the development of game theory and his name is associated with one of its most fundamental concepts: Nash equilibrium. As game-theoretic principles have become central to contemporary economics, Nash can be said to have exerted an enormous influence on the discipline.15 Indeed, his fellow Laureates Harsanyi and Selten have acknowledged their own debt to his pioneering contributions (see Harsanyi’s comments in Nash’s Nobel Seminar – Kuhn et al., 1996, p. 166). Nash’s work has also been applied in other social science contexts and in evolutionary biology (Kuhn et al., 1996; Milnor, 1998). Game theory is concerned with analysing strategic interaction between individuals or agents where decision making by each party is conditioned by the choices made and the actions taken by others. This kind of interaction is common in economic contexts: between competing firms, employers and workers, tax authorities and taxpayers, monetary authorities and economic agents, and so on. The first modern treatment of game theory in economics was John von Neumann and Oskar Morgenstern’s Theory of Games and Economic Behaviour, first published in 1944. This study focused on zero-sum two-person games that were later characterised by Nash as cooperative in nature: that is, participants are able to negotiate with each other to reach mutually acceptable outcomes. Nash’s PhD thesis (Nash, 1950a) both introduced the more widely applicable concept of a non-cooperative finite game where there is no communication or collusion between players, and identified the notion of what he called ‘equilibrium point’. This is the famous Nash equilibrium – a constellation of strategies between n-players from which no participant has an incentive to deviate because none can bring about an individual improvement by changing their personal strategy. Nash also provided proof that at least one such equilibrium always exists. Reporting some of the findings in his PhD thesis, the relevant papers here are Nash (1950b; 1951).

One aspect of Nash equilibrium specifically referenced in Nash’s Nobel citation concerns the alternative ways in which equilibrium may be interpreted (Royal Swedish Academy of Sciences, 1995). In his PhD thesis, Nash proposed two interpretations: one based on the concept of rationality and a second reflecting what he called ‘mass action’ (van Damme and Weibull, 1995). Under the rational interpretation, players are understood to act on the basis of knowledge of the full structure of the game, including accurate expectations about the choices of others. Given such conditions, Nash equilibrium emerges as players attempt to maximise their utility in the light of each other’s strategic dispositions. This has been the standard interpretation of Nash equilibrium in the literature as it was this that Nash deployed in his earliest published work; the mass-action alternative, resting quietly in his thesis, has been little noticed until recently (Kuhn et al., 1996).

The mass-action interpretation allows that players need be neither rational nor informed about the structure of a repeated game. In these circumstances ‘participants … accumulate empirical information on the relative advantages of the pure strategies at their disposal’ (Nash, quoted in Kuhn et al., 1996, p. 171). Here players are representative of the group interests that, Nash argues, characterise certain situations in economics or international politics (see van Damme and Weibull, 1995). The outcome is an equilibrium point arising from the ‘average behaviour’ in each of the group populations. Games of this form have also been used in biology as a means to understand the processes underpinning natural selection (Royal Swedish Academy of Sciences, 1995).

Nash’s other contributions to economics acknowledged by the Royal Swedish Academy include his bargaining solution for cooperative games (Nash, 1950c). As noted, the work for this paper was actually begun while Nash was still an undergraduate at Carnegie and was prompted by his only formal training in economics – the elective he took in international economics. Nash also initiated work that has sought to understand cooperative games by modelling their negotiation using a non-cooperative framework; this approach is known as the ‘Nash program’ (see Nash, 1951, and for its application, see Nash, 1953; for its significance, see Gul, 1997; Kuhn et al., 1996). Nash’s papers have been collected in Nash (1996) and, with editorial introductions, in Kuhn and Nasar (2002). Nash’s biographer is Nasar (1998).

Main Published Works

(1950a), ‘Non-Cooperative Games’, unpublished PhD Thesis, Princeton University.

(1950b), ‘Equilibrium Points in n-Person Games’, Proceedings of the National Academy of Sciences, 36, pp. 48–9.

(1950c), ‘The Bargaining Problem’, Econometrica, 18, pp. 155–62.

(1951), ‘Non-Cooperative Games’, Annals of Mathematics, 54 (2), pp. 286–95.

(1953), ‘Two-Person Cooperative Games’, Econometrica, 21, pp. 128–40.

(1996), Essays on Game Theory (Introduction by K. Binmore), Cheltenham, UK and Brookfield, USA: Edward Elgar.  

Secondary Literature

Gul, F. (1997), ‘A Nobel Prize for Game Theorists: The Contributions of Harsanyi, Nash and Selten’, Journal of Economic Perspectives, 11, Summer, pp. 159–74.

Kuhn, H.W., J.C. Harsanyi, R. Selten, J.W. Weibull, E. van Damme, J.F. Nash Jr and P. Hammerstein

(1996), ‘The Work of John Nash in Game Theory’, (Nobel Seminar, 8 December 1994), Journal of Economic Theory, 69, April, pp. 153–85.

Kuhn, H.W. and S. Nasar (eds) (2002), The Essential John Nash, Princeton, NJ: Princeton University Press.

 Leonard, R.J. (1994), ‘Reading Cournot, Reading Nash: The Creation and Stabilisation of the Nash Equilibrium’, Economic Journal, 104, May, pp. 492–511.

Milnor, J.(1998), ‘John Nash and “A Beautiful Mind”’, Notices of the American Mathematical Society, 45, November, pp. 1329–32.

Myerson, R.B. (1999), ‘Nash Equilibrium and the History of Economic Theory’, Journal of Economic Literature, 37, September, pp. 1067–82.

Nasar, S. (1998), A Beautiful Mind: A Biography of John Forbes Nash Jr., New York: Simon & Schuster.

Royal Swedish Academy of Sciences (1995), ‘The Nobel Memorial Prize in Economics 1994’, Scandinavian Journal of Economics, 97 (1), pp. 1–7.

Rubinstein, A. (1995), ‘John Nash: The Master of Economic Modeling’, Scandinavian Journal of Economics, 97 (1), pp. 9–13.

van Damme, E. and J.W. Weibull (1995), ‘Equilibrium in Strategic Interaction: The Contributions of John C. Harsanyi, John F. Nash and Reinhard Selten’, Scandinavian Journal of Economics, 97 (1), pp. 15–40.