A Beautiful Mind
Page 64
34. A. Nash, interview, 5.16.95.
35. Armand Borel, interview, 3.1.96.
36. Moore, interview, 10.5.94.
37. G. Borel, interview, 10.94.
38. John David Stier, interview, 9.20.97.
39. Letter from Alicia Nash to Arthur Mattuck, 11.27.71.
40. J. D. Stier, interview.
41. Norton Starr, professor of mathematics, Amherst College, interviews, 7.95 and 1.20.98.
42. Eleanor Stier, interview, 3.18.96.
43. John Stier, interview, 1.21.98.
44. Letter from John Nash to Arthur Mattuck, 1.1 5.73.
45. E. Stier, interview, 3.18.96.
46. Irving I. Gottesman, professor of psychology, University of Virginia, interview, 1.16.98.
47. Kenneth L. Fields, professor of mathematics. Rider University (formerly Rider College), interview, 1.30.98.
48. Melvvn B. Nathanson, professor of mathematics, Graduate Center of the City University of New York, interview, 1.31.98.
49. John C. M. Nash (with Melvvn B. Nathanson), “Cofinite Subsets of Asymptotic Bases for the Positive Integers,” Journal of Number Theory, vol. 20, no. 3 (1985), pp. 363–72; John C. M. Nash, “Results in Bases in Additive Number Theory,” Ph.D. thesis, Rutgers University, 1985.
50. John C. M. Nash, “Some Applications of a Theorem of M. Kneser,” Journal of Number Theory, vol. 44, no. 1 (1993), pp. 1–8.
51. John C. M. Nash, “On B4 Sequences,” Canadian Mathematical Bulletin, vol. 32, no. 4 (1989), pp. 446–49.
52. Alicia Nash, interview, 9.97.
Part Five: THE MOST WORTHY
47: Remission
1. Peter Sarnak, professor of mathematics, Princeton University, interview, 8.25.95.
2. E-mail from John Nash to Harold Kuhn, 6.20.96.
3. Hale Trotter, interviews, 11.29.95 and 9.10.97.
4. Mark Dudey, professor of economics, Rice University, interviews, 10.94 and 6.24.95.
5. Daniel Feenberg, interview, 10.94.
6. Letter from Edward G. Nilges to author, 8.19.95.
7. Lloyd S. Shapley, interview, 10.94.
8. George Winokur and Ming T. Tsuang, The Natural History of Mania, Depression and Schizophrenia (Washington, D.C.: American Psychiatric Press, 1996), p. 28.
9. Letter from John Nash to Richard Keefe, 1.14.95. Nash gives Johnny’s diagnosis as “paranoid schizophrenia” and “schizo-affective disorder.”
10. See, for example, Irving I. Gottesman, Schizophrenia Genesis, op. cit., p. 18; Michael R. Trimble, Biographical Psychiatry (New York: John Wiley & Sons, 1996), pp. 184–85.
11. John Forbes Nash, Jr., Les Prix Nobel 1994, op. cit.
12. John Nash, plenary lecture, World Congress of Psychiatry, Madrid, 8.26.96, op. cit.
13. Harold Kuhn, interview, 9.95.
14. Letter from John Nash to Richard Keefe, 1.14.95. Nash has made the same point to many people.
15. Winokur and Tsuang, op. cit., p. 30; also Manfred Bleuler, The Schizophrenic Disorders: Long-Term Patient and Family Studies (New Haven: Yale University Press, 1978).
16. Gerd Huber, Gisela Gross, Reinhold Schuttler, and Maria Linz, “Longitudinal Studies of Schizophrenic Patients,” Schizophrenia Bulletin, vol, 6, no. 4 (1980).
17. C. M. Harding, G. W. Brooks, T. Ashikaga, J. S. Strauss, and A. Brier, “The Vermont Longitudinal Study of Persons with Severe Mental Illness, I and II,” American Journal of Psychiatry, vol. 144 (1987), pp. 718–26, 727–35. E. Johnstone, D. Owens, A. Gold et al., “Schizophrenic Patients Discharged from Hospital: A Follow-Up Study,” British Journal of Psychiatry, no. 145 (1984), pp. 586–90, found that 18 percent of the 120 in the study had no significant symptoms and were functioning satisfactorily; 50 percent were still psychotic; and the remainder were somewhere in between. Only two subjects, both of whom had been hospitalized only once, were considered truly well.
18. Richard Wyatt, head of neuropsychiatry, National Institute of Mental Health, personal communication, 12.97. See also Winokur and Tsuang, op. cit., pp. 199–217.
19. Winokur and Tsuang, op. cit., pp. 267–68.
20. Huber et al., op. cit.
21. Richard Wyatt, interview, 5.5.96.
22. E. Fuller Torrey, Surviving Schizophrenia, op. cit.
23. E-mail from J. Nash to H. Kuhn, 6.1.95.
24. John Forbes Nash, Jr., Les Prix Nobel 1994, op. cit.
25. Letter from J. Nash to R. Keefe.
26. John Forbes Nash, Jr., Les Prix Nobel 1994, op. cit.
27. Social Science Citation Index, various dates.
28. John Conway, professor of mathematics, Princeton University, interview, 10.94.
29. Nash’s work on Riemannian embeddings and partial differential equations would likely have made him a strong candidate for a Fields in the 1960s and his contributions to game theory might easily have been honored with a Nobel as early as 1983, when Gerard Debreu won for his work on general equilibrium theory. He would certainly have garnered lesser honors such as membership in the National Academy of Sciences and the American Academy of Arts and Sciences.
30. Amartya Sen, professor of economics. Harvard University, interview, 12.92.
31. Fellows of the Econometric Society as of January 1988, Econometrica, vol. 56, n. 3 (May 1988).
32. Ariel Rubinstein, professor of economics, University of Tel Aviv and Princeton University, interviews, 1.96 and 2.96.
33. Mervyn King, professor of economics, London School of Economics, and vice-chairman, Bank of England, interview, 2.28.96.
34. Letter from Julie Gordon, executive director, The Econometric Society, to author, 2.2.96.
35. King, interview.
36. Interviews with Gary Chamberlain, professor of economics, Harvard University, 2.28.96; Beth E. Allen, professor of economics, University of Minnesota, 2.26.96.
37. Letter from Truman Bewley, professor of economics, Yale University, to Ariel Rubinstein, undated (spring 1989).
38. Ibid., 6.4.89.
39. Truman Bewley, interview, 2.20.96.
40. John Dawson, Logical Dilemmas: The Life and Work of Kurt Gödel, op. cit.
41. Ibid.
42. Ken Binmore, Roger Myerson, Ariel Rubinstein, “Nomination of Candidates as a Fellow,” 1990.
43. Letter from J. Gordon to author, 1.31.96.
48: The Prize
1. Jörgen W. Weibull, Stockholm School of Economics and member economics prize committee, interview, 11.14.96.
2. Ibid.
3. Carl-Olof jacobson, secretary-general of the Royal Swedish Academv of Sciences, interview, 2.12.97.
4. Kenneth Birnum, game theorist at the London School of Economics, for example, recently wrote to Harold Kuhn (e-mail, 1.7.98) that he had nominated Nash for the Nobel once in the 1980s. “I didn’t persist in nominating him because nobody seemed to take the idea seriously.”
5. Statutes of the Nobel Foundation, 4.27.95.
6. Michael Sohlman, executive director, Nobel Foundation, interview, 2.11.97.
7. Ibid.
8. Karl-Goran Mäler, executive director, Beijer Institute of the Royal Swedish Academy of Sciences, interview, 2.12.97.
9. Assar Lindbeck, “The Prize in Economic Science in Memory of Alfred Nobel,” Journal of Economic Literature, vol. 23 (March 1985), pp. 37–56.
10. Harriet Zuckerman, Scientific Elite: Nobel Laureates in the United States (London: Free Press, 1977).
11. Lindbeck, op. cit.
12. See, for example, John E. Morrill, “A Nobel Prize in Mathematics,” The American Mathematical Monthly, vol. 102, no. 10 (December 1995).
13. Lars Gårding and Lars Hörmander, “Why Is There No Nobel Prize in Mathematics?” The Mathematical Intelligencer (July 1985), pp. 73–74.
14. Jacobson, interview.
15. The sketch of Lindbeck is based on the author’s interview with him in Stockholm on 2.12.97, two autobiographical essays, and the impressions of members of the prize committee and the Academv of Sciences, including Carl-Olof Jacobson, 2.12.
97; Karl-Gustaf Löfgren, professor of economics, University of Umea, 2.12.97; Karl-Goran Mäler, 2.12.97; Jörgen Weibull and Torsten Persson, visiting professor, Harvard University, 10.4.94 and 3.7.97.
16. Persson, interview, 3.7.97.
17. Löfgren, interview.
18. Mäler, interview.
19. Lindbeck, “The Prize in Economic Science,” op. cit.
20. Löfgren, interview.
21. Kerstin Fredga, as told to Harold Kuhn at the 12.94 Nobel ceremony in Stockholm, 1.95.
22. By the late 1980s, Harold Kuhn and other game theorists were nominating Nash. Others, however, saw no point in doing so. “I did not nominate him,” Shubik later recalled. “He was better than several of the people I nominated, but it seemed that they’d throw him out because he’s nuts. The other reason was that I thought the bargaining work was better than the stuff on noncooperative equilibrium,” interview, 12.13.96.
23. Lindbeck, interview, 2.12.97.
24. Ariel Rubinstein, interview, 6.26.95.
25. Ariel Rubinstein, “Perfect Equilibrium in a Bargaining Model,” Econometrica, no. 50 (1982), pp. 97–109.
26. Rubinstein, interview, 6.95.
27. Weibull, interview, 1.14.96.
28. Ibid.
29. Ibid.
30. E-mail from Eric Fisher, assistant professor of economics, Ohio State University, to author, 7.25.95.
31. Weibull, interview, 11.6.96.
32. Gene Grossman, professor of economics, Princeton University, interview, 9.93. Grossman was the first to point out to the author, a reporter at The New York Times, that Nash might share a Nobel.
33. Nobel Symposium on Game Theory: Rationality and Equilibrium in Strategic Interaction, Bjork-born, Sweden, June 18–20, 1993.
34. Confidential source who attended the conference.
35. Persson, interview.
36. Confidential source who attended the conference.
37. Fax from Jörgen Weibull to Harold Kuhn, 7.14.93.
38. Letter from Robert J. Leonard to Harold Kuhn, 7.27.93.
39. Jacobson, interview.
40. Lindbeck, interview.
41. Ibid.
42. Confidential source.
43. Jacobson, interview.
44. Löfgren, interview.
45. Lindbeck, interview.
46. Ibid.
47. Ibid.
48. Shapley’s most important work is in cooperative game theory while Schelling’s work is in applications of game theory.
49. Lindbeck, interview.
50. Ibid.
51. The sketch of Stahl is based on interviews with his brother Ingolf Stahl, 2.12.97; Mäler; Lindbeck; Löfgren; Weibull; David Warsh, columnist, Boston Globe, 2.5.97; and others.
52. Ingemar Stahl, professor of law, Lund University, interview, 2.4.97.
53. Letter from Lars Hörmander to Ingemar Stahl, 9.10.93, with Nash bibliography.
54. Ibid.
55. Ingemar Stahl, interview.
56. Ibid.
57. Ibid.
58. Confidential source present at the discussion.
59. Ibid.
60. Ingemar Stahl, interview.
61. Confidential source.
62. Ibid.
63. Interviews with Lindbeck and Jacobson.
64. Weibull, interview.
65. Confidential source.
66. David Warsh, “Came Theory Plays Strategic Role in Economies’ Most Interesting Problems,” Chicago Tribune, 7.24.94.
67. Christer Kiselman, professor of mathematics, University of Uppsala, interview, 3.5.97.
68. Ibid.
69. Confidential source.
70. Weibull, interview, 11.6.96.
71. Lindbeck, interview.
72. Ibid.
73. Ibid.
74. Jacobson, interview.
75. Confidential source.
76. Lindbeck, interview.
77. Ibid.; also confidential source.
78. As quoted by Harold Kuhn, interview, 1.95.
79. E-mail from Harold Kuhn to Harold Shapiro, president, Princeton University, 9.1.94.
80. Confidential source.
81. Erik Dahmen, professor of economics, Stockholm Institute of Economics, and member, Roval Swedish Academy of Sciences, interview, 2.12.97.
82. Confidential source.
83. Anders Karlquist, interview, 3.17.97.
84. Lars Cårding, professor of mathematics, Lund University, personal communication, 2.10.97.
85. Bengt Nagel, personal communication, 2.10.97.
86. Confidential source.
87. Kjell Olof Feldt, “I Nationalekonomns Atervandsgrand,” Moderna Ticlcr (March 1994).
88. Karlquist, interview.
89. Confidential source.
90. Lindbeck, interview.
91. Confidential source.
92. Ibid.
93. Statutes of the Nobel Foundation.
94. Confidential source.
95. Ibid.
96. Jacobson, interview.
97. Confidential source.
98. Jacobson, interview.
99. Ingemar Stahl, interview.
100. Sohlman, interview.
101. Johann Schuck, reporter, article in Dagens Nyheter, 12.10.94. Schuck broke the storv of the behind-the-scenes fight between Stahl and Lindbeck that delayed the announcement of the prize. A translation was provided by Hans Carlsson, professor of economics, Lund University, 12.4.95.
102. Confidential source.
103. Ibid.
104. Harold Kuhn informed Alicia Nash on Friday, October 7, and Nash himself on October 10, the day before the official announcement.
105. Kiselman, interview.
106. Confidential source with access to the report.
107. Confidential source.
108. Ibid.
109. Confidential source with access to the report.
110. Confidential source.
111. Jacobson, interview.
112. Mäler, interview.
113. Jacobson, interview.
114. Ibid.
49: The Greatest Auction Ever
1. Harold Kuhn, interview, 1.95.
2. William Safire, “The Greatest Auction Ever,” New York Times, 3.16.95, as quoted by Paul Milgrom, Auction Theory’ for Privatization (New York: Cambridge University Press, forthcoming).
3. Edmund Andrews, “Wireless Bidders Jostle for Position,” New York Times, 12.5.94.
4. Milgrom, Auction Theory for Privatization, op. cit.
5. Michael Rothschild, dean of the Woodrow Wilson School, remarks at conference, “Market Design: Spectrum Auctions and Beyond,” Princeton University, 11.9.95.
6. Peter C. Cramton, “Dealing with Rivals? Allocating Scarce Resources? You Need Game Theory” (Xerox, 1994). Nash provided the fundamental theory used to analyze and predict behavior in simple games in which rational players have complete knowledge of each other’s preferences and abilities. Harsanyi, in papers published in 1967 and 1968, analyzed games in which some parties had private information. Selten, in 1976, extended the theory to dynamic games, games that take place over time. Cramton gives the offers and counteroffers during a merger negotiation as an example of a dynamic game.
7. Peter Passell, “Game Theory Captures a Nobel,” New York Times, 10.12.94.
8. Paul Samuelson as quoted by Vincent P. Crawford, “Theory and Experiment in the Analysis of Strategic Interaction,” Symposium on Experimental Economics, Econometric Society, Seventh World Congress, August 1995 (draft: September 1994).
9. See, for example, Robert Gibbons, “An Introduction to Applicable Game Theory,” Journal of Economic Perspectives, vol. 11, no. 1 (Winter 1997), pp. 127–49.
10. Avinash Dixit, interview, 7.97.
11. Avinash Dixit, as quoted by Passell, op. cit.
12. Ibid.
13. John McMillan, Games, Strategies and Managers (New York: Oxford University Press, 1992).
14. R. H. Coase, “The Federal Comm
unications Commission,” Journal of Law and Economics (October 1959), pp. 1–40, quoted by John McMillan, “Selling Spectrum Rights,” Journal of Economic Perspectives, vol. 8, no. 3 (Summer 1994).
15. Peter C. Cramton, “The PCS Spectrum Auction: An Early Assessment,” The Economist (August 25, 1995).
16. Milgrom, Auction Theory for Privatization, op. cit.
17. Ibid. See also McMillan, “Selling Spectrum Rights,” op. cit., pp. 153–55.
18. Ibid.
19. See, for example, McMillan, “Selling Spectrum Rights,” op. cit.; Paul Milgrom, “Game Theory and Its Use in the PCS Spectrum Auction,” Games ’95, conference, Jerusalem, 9.29.95.
20. Milgrom, Auction Theory for Privatization, op. cit.
21. Ibid.
22. Ibid.
23. Ibid.
24. McMillan, “Selling Spectrum Rights,” op. cit.
50: Reawakening
1. Sylvain Cappell, interview, 2.29.96.
2. Jörgen Weibull, interview, 11.14.96.
3. Harold and Estelle Kuhn, interviews, 1.95.
4. Weibull, interview.
5. Lena Koster, “For the First Time in 30 Years: Economy Prize Winner Lectured in Uppsala,” Uppsala Nya Tidning, 12.94.
6. Christer Kiselman, interview, 3.4.97.
7. Weibull, interview.
8. John Forbes Nash, Jr., Les Prix Nobel 1994, op. cit.
9. As quoted by Harold Kuhn, interview, 7.24.96.
10. E-mail from John Nash to Harold Kuhn, 3.26.96.
11. John Nash, plenary lecture, World Congress of Psychiatry, Madrid, 8.26.96, op. cit.
12. E-mail from J. Nash to H. Kuhn, 11.94.
13. Ibid., 8.6.95 and 8.26.95.
14. Harold Kuhn, interview, 1.95.
15. Armand Borel, interview, 3.1.96.
16. This conversation took place in a taxi on the way to Newark Airport on 12.5.94 and was recounted by Harold Kuhn, interview, 1.95.
17. As quoted by H. Kuhn, interview, 1.95.
18. E-mail from John Nash to Herbert Meltzer, 7.8.97.
19. E-mail from J. Nash to H. Kuhn, 7.16.95.
20. Confidential source.
21. E-mail from J. Nash to H. Kuhn, 5.12.95.
22. Alicia Nash, interview, 5.16.95.
23. H. Kuhn, interview, 7.26.95.
24. Avinash Dixit, personal communication, 1.31.96.
25. E-mail from J. Nash to H. Kuhn, 8.6.95.