A Beautiful Mind Part 22

26. Tucker, interview, 10.94.

27. Ibid.

28. Ibid.

29. John Nash, Les Prix n.o.bel 1994, Les Prix n.o.bel 1994, op. cit. 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, The New Pal-grave, op. cit. op. cit.

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

35. Ibid.

36. n.o.bel citation.

37. Avinash Dixit and Barry Nalebuff, Thinking Strategically, Thinking Strategically, op. cit. 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, "n.o.bel Seminar," Les Prix n.o.bel 1994, Les Prix n.o.bel 1994, op. cit., p. 288. 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 Theory of Games and Economic Behavior directs readers to Nash's work on noncooperative games, p. vii. 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, 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). 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 Broca's Brain (New York: Random House, 1979). (New York: Random House, 1979).

3. David Halberstam, The Fifties, The Fifties, op. cit. 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, Annals of Mathematics, no. 24 (1950). no. 24 (1950).

31. "To some extent there was a compet.i.tion between Nash, Shapley, and me," Shubik, interview, 12.13.96.

32. Shapley, interview.

33. Shapley, Additive and Non-Additive Set Functions, 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 Ph.D. thesis, Princeton University, 1953. Shapley published his famous result - the so-called Shapley value - a value for n 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 Econometrica in 1953 but actually written in August 1950 during Nash's first summer at RAND. 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 Bohnenbl.u.s.t, 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 Fortune (March 1951). (March 1951).

2. William Poundstone, Prisoner's Dilemma, Prisoner's Dilemma, op. cit.; Fred Kaplan, op. cit.; Fred Kaplan, The Wizards of Armageddon, The Wizards of Armageddon, op. cit.; op. cit.; The RAND Corporation: The First Fifteen Years The RAND Corporation: The First Fifteen Years (Santa Monica, Calif.: RAND, November 1963) and (Santa Monica, Calif.: RAND, November 1963) and 40th Year Anniversary 40th Year Anniversary (Santa Monica: RAND, 1963); John D. Williams, An Address, 6.21.50; Bruce L. R. Smith, (Santa Monica: RAND, 1963); John D. Williams, An Address, 6.21.50; Bruce L. R. Smith, The RAND Corporation The RAND Corporation (Cambridge: Harvard University Press, 1966); Bruno W. Augenstein, (Cambridge: Harvard University Press, 1966); Bruno W. Augenstein, A Brief History of RANDs Mathematics Department and Some of Its Accomplishments A Brief History of RANDs Mathematics Department and Some of Its Accomplishments (Santa Monica, Calif.: RAND, March 1993); Alexander M. Mood, "Miscellaneous Reminiscences," (Santa Monica, Calif.: RAND, March 1993); Alexander M. Mood, "Miscellaneous Reminiscences," Statistical Science, Statistical Science, vol. 5, no. 1 (1990), pp. 4041. vol. 5, no. 1 (1990), pp. 4041.

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

4. Isaac Asimov, Foundation Foundation (New York: Bantam Books, 1991). (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 The Question of National Defense (New York: Random House, 1959), as quoted in Poundstone, op. cit., pp. 8485. (New York: Random House, 1959), as quoted in Poundstone, op. cit., pp. 8485.

9. McDonald, "The War of Wits," op. cit.

10. The account of RND's beginnings is based on Poundstone, op. cit.

11. Ibid., p. 93.

12. See, for example, Stanislaw Ulam, Adventures of a Mathematician, Adventures of a Mathematician, op. cit.; Richard Rhodes, op. cit.; Richard Rhodes, The Making of the Atomic Bomb The Making of the Atomic Bomb (New York: Simon & Schuster, 1986); Hodges, (New York: Simon & Schuster, 1986); Hodges, Alan Turing: The Enigma, Alan Turing: The Enigma, op. cit. 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 Great Economists Since Keynes (Totowa, N.J.: Barnes & n.o.ble, 1985), pp. 69. (Totowa, N.J.: Barnes & n.o.ble, 1985), pp. 69.

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

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

28. Ibid.

29. Ibid., p. 46.

30. Kaplan, op. cit.

31. Martha Dresner, interview.

32. Best, interview.

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

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

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