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# Nash, John 1928–

BIBLIOGRAPHY

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 Nasars biography A Beautiful Mind: A Biography of John Forbes Nash Jr. published in 1998. A popular movie in 2001 presented a fictional version of Nashs 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 players 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. Nashs 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 Nashs 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

## BIBLIOGRAPHY

### PRIMARY WORKS

Nash, John F. 1950a. The Bargaining Problem. Econometrica 18 (2): 155162.

Nash, John F. 1950b. Equilibrium Points in N-Person Games. Proceedings of the National Academy of Sciences U.S.A. 36 (1): 4849.

Nash, John F. 1951. Noncooperative Games. Annals of Mathematics 54 (2): 289295.

Nash, John F. 1953. Two-Person Cooperative Games. Econometrica 21 (1): 128140.

### SECONDARY WORKS

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): 10671082.

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, 1342. Princeton, NJ: Princeton University Press. Originally published in German in 1928 as Zur Theorie der Gesellschaftsspiele (Mathematische Annalen 100: 295320).

Roger B. Myerson

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## Nash, John

Nash, John (1752–1835). English architect, master of scenography, urban designer, and important architect of the Picturesque. He trained in the office of Sir Robert Taylor before setting up on his own in 1775 as a designer and builder of stucco-fronted houses. Bankrupted in 1783, he moved to Wales, where he met Uvedale Price and was initiated into the cult of the Picturesque. While there he designed the County Gaol, Carmarthen (1789–92—demolished), and other buildings, and became so busy he had to take on A. C. Pugin, then a refugee, as a draughtsman. He returned to London in 1796 and formed a partnership with Humphry Repton, the fashionable landscape-gardener, who had ample opportunities to pick up architectural commissions. Between them they remodelled many country seats and grounds, enhancing their Picturesque qualities, before the partnership was dissolved in 1802. Nash went from strength to strength, designing many houses and villas, including Killymoon Castle, Co. Tyrone (c.1801–3—castellated with round arches), the very pretty Cronkhill, Shlop. (c.1802—Italianate and asymmetrical), and Caerhayes Castle, Cornwall (c.1808—castellated). These asymmetrical compositions were influenced by Payne Knight's important house, Downton Castle, Herefs. (begun 1772). Nash built an estate of cottages at Blaise Hamlet, near Bristol (1810–11), the prototype of the Picturesque village, with a heady brew of thatch, leaded lights, elaborate chimneys, asymmetry, and ‘rustic’ architecture loosely based on vernacular forms.

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.

Bibliography

Ballantyne (1997);
Colvin 1995);
Colvin (ed.) (1973);
T. Davis (1973);
Freer (1993);
Hobhouse (1975);
Mansbridge (1973);
Middleton & and Watkin (1987);
Musgrave (1959);
Placzek (ed.) (1982);
H. Roberts (1939);
Summerson (ed.) (1980a);
Temple (1979);
Jane Turner (1996)

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## Nash, John Henry

John Henry Nash, 1871–1947, American printer and bibliophile, b. Woodbridge, Canada. After learning the printer's trade, he emigrated to the United States in 1894. He eventually became professor of typography at the Univ. of Oregon. Nash published finely crafted editions of several works, including The Divine Comedy (1929), Benjamin Franklin's Autobiography, and the Vulgate (1932). He was famous for his collection of books with handmade bindings.

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## Nash, John

Nash, John (1752–1835) English architect and town planner, an important figure in the Regency style. He designed Regent's Park and Regent Street, London, and rebuilt the Royal Pavilion, Brighton (1815–23).

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