Nash, John 1928 –
In a few short papers between 1950 and 1953, John F. Nash Jr. formulated two major concepts of game theory: the Nash bargaining solution and Nash equilibrium. His formulation of noncooperative equilibrium was one of the greatest conceptual breakthroughs in social science. Nash then turned his focus to mathematical analysis and made important contributions to the theory of manifolds. His work was tragically interrupted by mental illness after 1960. Decades later, his recovery and return to active work was widely celebrated in the field of economics, where his ideas had triumphed even in his absence. (See Sylvia Nasar’s biography A Beautiful Mind: A Biography of John Forbes Nash Jr. published in 1998. A popular movie in 2001 presented a fictional version of Nash’s life.)
The Nash bargaining solution (1950a, 1953) is a general theory of efficient and equitable outcomes for two-person bargaining problems. A bargaining problem is characterized by a convex set of allocations that are feasible for the players, where each allocation is a pair of numerical payoffs, one for each player. Letting 0 represent the payoff that a player could get without any cooperative agreement, we assume that the allocation (0, 0) is in the feasible set.
In simple examples where both players’ payoffs are measured in transferable units of money, a reasonable solution would divide equally the amount that they can earn by cooperating. But Nash argued that when payoffs are not transferable, a reasonable solution should remain invariant when the scale in which a player’s payoffs are measured is multiplied by a positive constant or when feasible alternatives other than the solution are eliminated. Remarkably, Nash proved that these properties are satisfied by a unique solution, which maximizes the multiplicative product of the players’ gains. Nash’s bargaining solution has become the cornerstone of the theory of cooperative games without transferable utility.
Nash equilibrium is a general solution concept for games in strategic form. A strategic-form game is defined by specifying the set of players, the set of strategies for each player, and the payoff that each player would get from every possible combination of strategies that the players could choose. A Nash equilibrium is a combination of strategies such that no player can increase his or her expected payoff by choosing a different strategy, when the other players’ strategies are held fixed. Nash (1950b, 1951) proved that any finite game has such noncooperative equilibria, when randomized strategies are admitted, and he argued that noncooperative equilibrium analysis should be a general methodology for analyzing games of any kind. In 1953 he worked to show how his cooperative bargaining theory could be based on equilibrium analysis of noncooperative games in which players independently choose their bargaining strategies.
The importance of Nash equilibrium is manifested when we consider any question about reforming any economic, political, or social institution. To reform an institution is to change the rules of the game that people play in this institution. A case for reform must depend on some predictions about how people would behave in this institution, with or without the reform. If a case for reform depended on a prediction that was not a Nash equilibrium, it could be undermined by an individual who recognizes that behaving differently would earn a better payoff. Such difficulties are avoided by analyzing and comparing Nash equilibria of different institutions.
Nash equilibrium formalizes basic economic assumptions concerning the intelligence and rationality of individuals. The assumption of payoff-maximizing individual behavior has been common in economic analysis since Augustin A. Cournot (1838). But Nash equilibrium also assumes the independence of individual decision-making, which was viewed as a restrictive assumption until John von Neumann (1928) presented a broader concept of strategic decision-making, in which a strategy is a complete plan of actions for a player in all possible contingencies (Myerson 1999). This concept of strategy was used in Nash’s argument that any dynamic bargaining process can be studied as a noncooperative game in which players plan their strategies independently before bargaining begins.
Later work in noncooperative game theory has refined and extended the equilibrium concept to take fuller account of sequential decision-making and communication in games. These developments broadened the analytical power of noncooperative game theory, which has transformed the scope of economics. Before Nash, many economists accepted a narrow definition of economics as being principally concerned with production and allocation of material goods. But noncooperative game theory provides a general framework for studying competition in any arena, and so economists have come to define their field more broadly, as being concerned with analysis of incentives in all social institutions. Thus by accepting game theory as a core analytical methodology alongside price theory, economic analysis has returned to the breadth of vision that characterized the ancient Greek social philosophers who gave economics its name.
SEE ALSO Equilibrium in Economics; Game Theory; Nash Equilibrium; Noncooperative Games; Strategic Games
Nash, John F. 1950a. The Bargaining Problem. Econometrica 18 (2): 155–162.
Nash, John F. 1950b. Equilibrium Points in N-Person Games. Proceedings of the National Academy of Sciences U.S.A. 36 (1): 48–49.
Nash, John F. 1951. Noncooperative Games. Annals of Mathematics 54 (2): 289–295.
Nash, John F. 1953. Two-Person Cooperative Games. Econometrica 21 (1): 128–140.
Cournot, Augustin A. 1838. Recherches sur les principes mathématiquess de la théorie des richesses. Paris: Hachette. Published in an English translation by Nathaniel T. Bacon as Researches into the Mathematical Principles of the Theory of Wealth (New York: Macmillan, 1927).
Myerson, Roger B. 1999. Nash Equilibrium and the History of Economic Theory. Journal of Economic Literature 37 (3): 1067–1082.
Von Neumann, John. 1959. On the Theory of Games of Strategy. In Contributions to the Theory of Games IV, trans. S. Bargmann, ed. R. D. Luce and A. W. Tucker, 13–42. Princeton, NJ: Princeton University Press. Originally published in German in 1928 as “Zur Theorie der Gesellschaftsspiele” (Mathematische Annalen 100: 295–320).
Roger B. Myerson
Nash was appointed architect to the Office of Woods and Forests (1806), and from this time was in favour with the Prince of Wales (later Prince Regent and King George IV (reigned 1820–30) ). He laid out Marylebone Park, London, an estate that reverted to the Crown in 1811, with proposals that became (1819) Regent's Park, an agreeably planted area around which were huge stucco-fronted palatial terraces and private villas. The façades of Cornwall and Clarence Terraces were designed by Decimus Burton, and Cumberland Gate and Terrace were built under James Thomson. Nash himself designed Ulster, York, Hanover, Kent, Chester, Cambridge, and St Andrew's Terraces, York Gate, Sussex Place, and Park Square (1821–30). Park Crescent was built 1812–22. Of the villas, Nash designed Hanover Lodge, and was responsible for the layout and many of the designs of the Park Villages (begun 1824), really a model suburb, completed by Pennethorne, and including Italianate and Picturesque barge-boarded inventions. So that the new Park should be connected to Westminster, Nash proposed a new street (Regent Street), linked to the existing Portland Place (1776–90—by James and Robert Adam) by means of a curved thoroughfare laid out around the ingenious portico and steeple of the Church of All Souls, Langham Place (1822–5—designed by Nash himself), then crossing Oxford Street and terminating (by means of The Quadrant) at Piccadilly Circus. The of The Quadrant) at Piccadilly Circus. The palatial blocks along the street were designed as scenographic events (begun 1813, but all destroyed and replaced.
Nash became personal architect to the Regent and remodelled the Royal Pavilion, Brighton, Sussex (1815–21), in the Hindoo and Chinese styles, exotically intermingled. Once the Prince became King in 1820, Nash was ordered to reconstruct Buckingham House (later Palace) on the most lavish scale: much of his work there (1820–30) survives, although the Mall front was twice changed, first by Blore and then by Aston Webb. Other designs include the Royal Opera Arcade, Haymarket (1816–18), the Haymarket Theatre (1820–1), Suffolk Street and Suffolk Place (1820s), Clarence House, St James's (1825–8), the United Services Club, Pall Mall (1826–8), the West Strand improvements opposite Charing Cross (1830–2), and Carlton House Terrace, the Mall (1827–33), which has a row of cast-iron Greek Doric columns on the Mall front. One of his most exquisite designs was Marble Arch, originally designed to stand in front of Buckingham Palace, but moved to its present inappropriate site in 1851.
Nash's works have suffered greatly from demolitions and alterations, and of his brilliant scheme linking Waterloo Place to Regent's Park very little remains of the architecture. His eclecticism, charm, scenographic effects, and widespread use of stucco did not find favour with younger architects, concerned as they were with purity, morality, expression of structure and materials, and the Gothic Revival. Yet he was the most successful civic designer London has ever had, and it is curious he has not had the appreciation he deserves, even from some of those who have written about him.
Colvin (ed.) (1973);
T. Davis (1973);
Middleton & and Watkin (1987);
Placzek (ed.) (1982);
H. Roberts (1939);
Summerson (ed.) (1980a);
Jane Turner (1996)
NASH, JOHN (1752–1835), English architect, developer, and city planner.
John Nash is best known for his work in creating London's Regent's Park and Regent Street. Throughout his long and prolific career Nash worked in a variety of styles, the result of two influences. The first was the classicism of Sir Robert Taylor (1714–1788), in whose offices he trained in the years before 1778. The second was the picturesque approach of landscape designer Humphry Repton (1752–1818), with whom Nash worked between 1792 and the early 1800s. For Repton, landscape design was much more than gardening, and his schemes for the estates of wealthy landowners would invariably include architectural elements designed to enhance the picturesque qualities of the landscape, in whatever style he felt best reflected the "true character" of the site. Nash provided the designs to fit, which ranged from neo-Palladian villas (Southgate Grove, Middlesex, 1797) to gothic castles (Luscombe Castle, Devon, 1800; Killymoon Castle, Ireland, c. 1803), and numerous picturesque thatched cottages (Blaise Hamlet, 1803–11). In each case considerations of a picturesque outline and the relationship of rooms to views over the landscape took precedence over classical symmetry or stylistic "correctness." To the discerning eye, Nash's gothic castles and cottages rarely appeared historically convincing, but Nash was interested in visual effects and historical associations, not in authenticity. His work with Repton played an important role in spreading and popularizing the gothic style.
In 1806 Nash was appointed architect to the Department of Woods and Forests, a post that involved the maintenance of the royal estates. In 1811 he proposed an ambitious scheme to create a park and a new residential quarter on the extensive crown lands in north London (Regent's Park, from 1812). Making a revolutionary break from the formal symmetrical squares that had been a feature of eighteenth-century London, Nash designed a romantic landscape of lakes, curving pathways, gentle slopes, and clumps of trees, with groups of houses scattered around the periphery. It was the first time the picturesque ideal of houses set within parkland had been applied at such a large scale to an urban setting, and it was
to be Nash's most influential work. Plans to build a new palace for the Prince Regent within the park came to nothing, but Nash went ahead with his own version, surrounding the park with spectacular "palaces," which were in fact simply row houses dressed up with elaborately articulated classical facades (Cumberland Terrace, 1826–1827).
A key component of Nash's scheme was the creation of a new ceremonial and commercial route (Regent Street, from 1813) between the new park and Carlton House, the Prince Regent's London residence situated more than a mile south of the park in St. James's. The complexities of land ownership in this crowded area of the city made a straight route impractical and Nash again applied picturesque principles by designing a curving street with a number of vistas and focal points. While Nash designed many of the key buildings, individual owners and developers were encouraged to design and build their own parts of the street frontage, leading to a rich and varied street-scape. It was a sharp contrast with the officially regulated conformity of contemporary developments in Paris (Rue de Rivoli, Charles Percier and Pierre-Francois-Leonard Fontaine, 1802–1805) and a practical illustration of a "democratic" approach to urbanism. As with the park, Regent Street was an influential example of the application of picturesque principles in an urban context.
Through his marriage to Mary Anne Bradley in 1798, Nash entered the social circle of the future Prince Regent, and over the following years he became the prince's favored designer. Their first collaboration was the prince's country retreat in Windsor—Royal Lodge (1812–1814), a lavish palace in the guise of a thatched cottage. Then came the prince's seaside villa (Brighton Pavilion, 1815–1823), which Nash rebuilt in a fantastical oriental style complete with onion domes and elaborate chinoiserie interiors. In 1820 the prince became King George IV (r. 1820–1830) and persuaded the government he needed a new palace in London. In 1825 Parliament, envisaging minor refurbishment works, voted £200,000 for Nash to convert the old Buckingham House into Buckingham Palace. But the king had more ambitious plans and Nash was caught between the king's escalating architectural ambitions and the government's desire to economize. Unable to satisfy either, and by then in his seventies, in 1831 he was forced to retire to the gothic castle he had built on the Isle of Wight (East Cowes Castle, 1798–1821).
Repton, Humphry. Observations on the Theory and Practice of Landscape Gardening. London, 1803.
Davis, Terence. John Nash, the Prince Regent's Architect. London, 1966.
Summerson, John. John Nash, Architect to King George IV. London, 1935.
——. Georgian London. London, 1945.