A Beautiful Mind (81 page)

23
. Harold Kuhn was for many years convinced that Nash had mailed a copv of his first draft to von Neumann while he was still at Carnegie. Also interviews with David Gale, 9.20.95, and William Browder, 12.6.96.

24
. After historian Robert Leonard published the established version of the origins of the paper in “Reading Cournot, Reading Nash: The Creation and Stabilisation of the Nash Equilibrium,”
The Economic Journal,
no. 164 (May 1994), p. 497, Nash corrected the record at a lunch with Harold Kuhn and Roger Myerson, 5.96, Kuhn, personal communication, 5.96.

25
. John Nash, “The Bargaining Problem,” op. cit., p. 155.

26
. John Nash,
Les Prix Nobel 1994,
op. cit., p. 277.

10: Nash’s Rival Idea

1
. Harold Kuhn, interview, 4.14.97.

2
. Albert William Tucker, interview, 10.94.

3
. The beer party scene was reconstructed from the recollections of Melvin Hausner, 2.6.96, Martin Davis, 2.20.96, and Hartley Rogers, 1.16.96, who attended several such parties in the course of their graduate school careers.

4
. Davis, interview.

5
. Ibid. Amazingly, Davis was able, forty years later, to recall the entire song, a few lines of which are given here, interview.

6
. Kuhn, interview, 4.16.97.

7
. Ibid.

8
. Henri Poincaré, quoted in E. T. Bell,
Men of Mathematics,
op. cit., p. 551.

9
. John Nash to Robert Leonard, e-mail, 2.20.93. Further details supplied by Harold Kuhn, interview, 4.17.97.

10
. “All the graduate students were afraid of him,” according to Donald Spencer, interview, 11.8.95.

11
. Von Neumann’s dress and manner are described by George Mowbry in a letter, 4.5.95. Harold Kuhn, interview, 5.2.97.

12
. See, for example, Norman McRae,
John von Neumann,
op. cit., pp. 350–56.

13
. As told to Harold Kuhn, 4.17.97.

14
. John Nash,
Les Prix Nobel 1994,
op. cit.

15
. Silvano Arieti,
Creativity,
op. cit., p. 294.

16
. J. Nash to R. Leonard, e-mail.

17
. Ibid.

18
. The conversation between Nash and Gale was recounted by Gale in an interview, 9.20.95. Gale also suggested that Nash use Kakutani’s fixed point theorem instead of Brouwer’s to simplify the proof, a suggestion that Nash followed in the note in the National Academy of Sciences
Proceedings.

19
. John F. Nash, Jr., “Equilibrium Points in N-Person Games,” communicated by S. Lefschetz, 11.16.49, pp. 48–49.

20
. Gale, interview.

21
. Tucker, interview, 10.94.

22
. Gian-Carlo Rota, interview, 12.12.95.

23
. Tucker’s account of Minsky’s thesis on computers and the brain, “Neural Networks and the Brain Problem,” is given in an interview with Stephen B. Maurer published in the
Two Year College Mathematics Journal
vol. 14, no. 3 (June 1983).

24
. Tucker, interview.

25
. Harold Kuhn, “Nobel Seminar,”
Les Prix Nobel 1994,
op. cit., p. 283.

26
. Tucker, interview, 10.94.

27
. Ibid.

28
. Ibid.

29
. John Nash,
Les Prix Nobel 1994,
op. cit.

30
. Tucker, interview.

31
. Letter from Albert W. Tucker to Solomon Lefschetz, 5.10.50.

32
. Ibid.

33
. See, for example, introduction, John Eatwell, Murray Milgate, and Peter Newman,
The New Pal-grave,
op. cit.

34
. “It so happens that the concept of the two-person zero-sum games has
very few
real life applications,” John C. Harsanyi, “Nobel Seminar,”
Les Prix Nobel 1994,
op. cit., p. 285.

35
. Ibid.

36
. Nobel citation.

37
. Avinash Dixit and Barry Nalebuff,
Thinking Strategically,
op. cit.

38
. Ibid.

39
. “Nowadays it almost seems to be obvious that the correct application of Darwinism to problems of social interaction among animals requires the use of non-cooperative game theory,” according to Reinhard Selten, “Nobel Seminar,”
Les Prix Nobel 1994,
op. cit., p. 288.

40
. “Game Theory,” in Eatwell, Milgate, and Newman, op. cit., p. xiii.

41
. Michael Intriligator, personal communication, 6.27.95.

42
. Selten, op. cit., p. 297.

43
. Von Neumann, as Nash always acknowledged, nonetheless helped to gain attention for Nash’s ideas. For example, the preface to the third edition (1953) of
Theory of Games and Economic Behavior
directs readers to Nash’s work on noncooperative games, p. vii.

11: Lloyd

1
. T. S. Ferguson, “Biographical Note on Lloyd Shapley,” in
Stochastic Games and Related Topics in Honor of Professor L. S. Shapley,
edited by T. E. S. Raghavan, T. S. Ferguson, T. Parthasarathy, and O. J. Vrieze (Boston: Kluwer Academic Publishers, 1989).

2
. See, for example, Carl Sagan,
Broca’s Brain
(New York: Random House, 1979).

3
. David Halberstam,
The Fifties,
op. cit.

4
. The description of Shapley’s experiences during the war, at Princeton, and at RAND draw on the recollections of Harold Kuhn, 11.18.96; Norman Shapiro, 2,9.96; Martin Shubik, 9.27.95 and 12.13.96; Melvin Hausner, 2.6.96; Eugenio Calabi, 3.2.96; John Danskin, 10.19.96; William Lucas, 6.27.95; Hartley Rogers, 1.26.96; John McCarthy, 2.4.96; Marvin Minsky, 2.13.96; Robert Wilson, 3.7.96; Michael Intriligator, 6.27.95.

5
. Letter from John von Neumann, 1.54.

6
. Solomon Leader, interview, 6.9.95.

7
. Rogers, interview, 1.26.96.

8
. “It was like ESP. Shapley seemed to know where all of the pieces were all of the time,” Minsky, interview.

9
. Hausner, interview, 2.6.96.

10
. Danskin, interview, 10.19.95.

11
. Letter from Lloyd Shapley to Solomon Lefschetz, 4.4.49.

12
. Interviews with Nancy Nimitz, 5.21.96, and Kuhn, 4.4.96.

13
. Shapiro, interview, 12.13.96.

14
. Intriligator, interview, 6.27.95.

15
. Shubik, interview, 12.13.96.

16
. Lloyd S. Shapley, interview, 10.94.

17
. Ibid.

18
. Shubik, interview, 12.13.96.

19
. Interviews with Shapley, Shubik, McCarthy, Calabi.

20
. Calabi, interview.

21
. Ibid.

22
. Ibid.

23
. Shubik, interview, 9.27.95.

24
. Shubik, interview, 9.27.95.

25
. Letter from Nash to Martin Shubik, undated (1950 or 1951).

26
. McCarthy, interview.

27
. McCarthy, interview.

28
. Hausner, interview, 2.6.96; M. Hausner, J. Nash, L. Shapley, and M. Shubik, “So Long Sucker — A Four-Person Game,” mimeo provided by Hausner.

29
. Interviews with Shubik and McCarthy.

30
. John Nash and Lloyd Shapley, “A Simple Three-Person Poker Game,”
Annals of Mathematics,
no. 24 (1950).

31
. “To some extent there was a competition between Nash, Shapley, and me,” Shubik, interview, 12.13.96.

32
. Shapley, interview.

33
. Shapley,
Additive and Non-Additive Set Functions,
Ph.D. thesis, Princeton University, 1953. Shapley published his famous result — the so-called Shapley value — a value for
n
-person games, in 1953.

34
. Martin Shubik, “Game Theory at Princeton,” op. cit., p. 6: “We all believed that a problem of importance was the characterization of the concept of threat in a two person game and the incorporation of the use of threat in determining the influence of the employment of threat in a bargaining situation. [Nash, Shapley, and I] worked on this problem, but Nash managed to formulate a good model of the two person bargain utilizing threat moves to start with.” Shubik is referring here to Nash’s “Two-Person Cooperative Games,” published in
Econometrica
in 1953 but actually written in August 1950 during Nash’s first summer at RAND.

35
. Letter from Albert W. Tucker, 1953

36
. Ibid.

37
. Letter from Frederick Bohnenblust, spring 1953.

38
. Letter from John von Neumann, 1.54.

39
. Kuhn, interview, 11.18.96.

40
. Shapley, interview, 10.94.

12: The War of Wits

1
. John McDonald, “The War of Wits,”
Fortune
(March 1951).

2
. William Poundstone,
Prisoner’s Dilemma,
op. cit.; Fred Kaplan,
The Wizards of Armageddon,
op. cit.;
The RAND Corporation: The First Fifteen Years
(Santa Monica, Calif.: RAND, November 1963) and
40th Year Anniversary
(Santa Monica: RAND, 1963); John D. Williams, An Address, 6.21.50; Bruce L. R. Smith,
The RAND Corporation
(Cambridge: Harvard University Press, 1966); Bruno W. Augenstein,
A Brief History of RANDs Mathematics Department and Some of Its Accomplishments
(Santa Monica, Calif.: RAND, March 1993); Alexander M. Mood, “Miscellaneous Reminiscences,”
Statistical Science,
vol. 5, no. 1 (1990), pp. 40–41.

3
. Herman Kahn,
On Thermonuclear War
(Princeton: Princeton Universih’ Press, 1960), as quoted in Poundstone, op. cit., p. 90.

4
. Isaac Asimov,
Foundation
(New York: Bantam Books, 1991).

5
. Poundstone, op. cit.

6
. Kaplan, op. cit., p. 52.

7
. Ibid., p. 10.

8
. Oskar Morgenstern,
The Question of National Defense
(New York: Random House, 1959), as quoted in Poundstone, op. cit., pp. 84–85.

9
. McDonald, “The War of Wits,” op. cit.

10
. The account of R\ND’s beginnings is based on Poundstone, op. cit.

11
. Ibid., p. 93.

12
. See, for example, Stanislaw Ulam,
Adventures of a Mathematician,
op. cit.; Richard Rhodes,
The Making of the Atomic Bomb
(New York: Simon & Schuster, 1986); Hodges,
Alan Turing: The Enigma,
op. cit.

13
. Mina Rees, “The Mathematical Sciences and World War II,” op. cit.

14
. The sketch of RAND’s mathematics, economics, and computer groups is based largely on interviews with RAND staff and consultants from the earlv Cold War period, including Kenneth Arrow, 6.26.95; Bruno Augenstein, 6.13.96; Richard Best, 5.22.96; Bernice Brown, 5.22.96; John Danskin, 10.19.95; Martha Dresner, 5.21.96; Theodore Harris, 5.24.96; Mario Juncosa, 5.21.96 and 5.24.96; William Karush, 5.96; William F. Lucas, 6.26.95; John W. Milnor, 9.95; John McCarthy, 2.4.96; Alexander M. Mood, 5.23.96; Evar Nering, 6.18.96; Nancy Nimitz, 5.21.96; Melvin Peisakoff, 6.3.96; Harold N. Shapiro, 2.20.96; Norman Shapiro, 2.29.96; Lloyd S. Shapley, 11.94; Herbert Simon, 10.16.95; Robert Specht, 2.96; Albert W. Tucker, 12.94; Willis H. Ware, 5.24.96; Robert W. Wilson, 8.96; Charles Wolf, Jr., 5.22.96.

15
. Augenstein, interview, 6.13.96.

16
. R. Duncan Luce, interview, 1996.

17
. The descriptions of Arrow’s contributions are taken from Mark Blaug,
Great Economists Since Keynes
(Totowa, N.J.: Barnes & Noble, 1985), pp. 6–9.

18
. Kenneth Arrow, professor of economics, Stanford University, interview, 6.26.95.

19
. McDonald, interview.

20
. Richard Best, former manager of security, RAND Corporation, interview, 5.22.96.

21
. Interviews with Alexander M. Mood, professor of mathematics, Universih of California at Irvine, former deputy director, mathematics department, RAND Corporation, 5.23.96, and Mario L. Juncosa, mathematician, RAND, 5.21.96 and 5.24.96.

22
. Kaplan, op. cit., p. 51.

23
. Bernice Brown, retired statistician, RAND, interview, 5.22.96.

24
. Augenstein, interview.

25
. Arrow, interview.

26
.
Chronicle of the Twentieth Century,
op. cit., p. 667.

27
. David Halberstam,
The Fifties,
op. cit.

28
. Ibid.

29
. Ibid., p. 46.

30
. Kaplan, op. cit.

31
. Martha Dresner, interview.

32
. Best, interview.

33
. Halberstam,
The Fifties,
op. cit., p. 45;
Chronicle of the Twentieth Century,
op. cit., p. 677.

34
. Halberstam, op. cit., p. 49.

35
.
Chronicle of the Twentieth Century,
op. cit., p. 750.

36
. Best, interview.

37
. Ibid.

38
. Letter from Col. Walter Hardie, U.S. Air Force, to RAND, 10.25.50.

39
. As told to Harold Kuhn, interview, 8.97.

40
. Letter from John Nash to John and Virginia Nash, 11.10.51.

41
. Best, interview.

42
. The Eisenhower guidelines refer to DOD directive 52206, 1953 and Executive Order 10450, 1953.

43
. Danskin, interview.

44
. Robert Specht, interview, 10.96.

45
. John Williams,
The Complcat Strategyst,
op. cit.

46
. The account of mathematicians’ work habits is based on interviews with Brown, Mood, Juncosa, Danskin, and Shapiro.