A Beautiful Mind Part 21

7. Kuhn, interview.

8. Ibid.; Hausner, interview.

9. Robert J. Leonard, "From Parlor Games to Social Science," op. cit.

10. See, for example, H. W. Kuhn and A. W. Tucker, "John von Neumann's Work in the Theory of Games and Mathematical Economics," Bulletin of the American Mathematical Society Bulletin of the American Mathematical Society (May 1958). (May 1958).

11. Leonard, "From Parlor Games to Social Science," op. cit.

12. Ibid.

13. Ibid.

14. Dorothy Morgenstern Thomas, interview, 1.25.96. Morgenstern kept a portrait of the kaiser hanging in his home.

15. Letter from George Mowbry to author, 4.5.95.

16. Leonard, "From Parlor Games to Social Science," op. cit.

17. As quoted in ibid.

18. Ibid.

19. Ibid.

20. Ibid.

21. Ibid.

22. Ibid.

23. Ibid.

24. Ibid.

25. A. W. Tucker, who knew both men well, said, "If he hadn't been forced to write a book, it wouldn't have gotten written," interview, 10.94. Von Neumann was interested in economics before he met Morgenstern.

26. Leonard, "From Parlor Games to Social Science," op. cit.

27. Ibid.

28. Von Neumann and Morgenstern, op. cit., p. 6.

29. Leonid Hurwicz, "The Theory of Economic Behavior," The American Economic Review The American Economic Review (1945), pp. 90925. (1945), pp. 90925.

30. Von Neumann and Morgenstern, op. cit., p. 7.

31. Ibid., p. 3.

32. Ibid.

33. Ibid., p. 4.

34. Ibid., p. 7.

35. Ibid., p. 2.

36. Ibid.

37. Ibid., p. 6.

38. New York Times, New York Times, 3.46. 3.46.

39. See, for example, Herbert Simon, The American Journal of Sociology, The American Journal of Sociology, no. 50 (1945), pp. 55860. Hurwicz, op. cit.; Jacob Marschak, "Neumann's and Morgenstern's New Approach to Static Economics," no. 50 (1945), pp. 55860. Hurwicz, op. cit.; Jacob Marschak, "Neumann's and Morgenstern's New Approach to Static Economics," Journal of Political Economy, Journal of Political Economy, no. 54 (1946), pp. 97115; John McDonald, "A Theory of Strategy," no. 54 (1946), pp. 97115; John McDonald, "A Theory of Strategy," Fortune Fortune (June 1949), pp. 100110. (June 1949), pp. 100110.

40. Leonard, "From Parlor Games to Social Science," op. cit.

41. Ibid.

42. Ibid.

43. Shubik, "Game Theory and Princeton," op. cit., p. 2.

44. Von Neumann and Morgenstern, op. cit. See also Eatwell, Milgate, and Newman, op. cit.

45. Von Neumann and Morgenstern, op. cit.

46. Ibid.

47. See, for example, John C. Harsanyi, "n.o.bel Seminar," in Les Prix n.o.bel 1994. Les Prix n.o.bel 1994.

48. Von Neumann and Morgenstern, op. cit.

49. Ibid.

50. Ibid.

51. Harsanyi, op. cit.

9: The Bargaining Problem

1. John Forbes Nash, Jr., "The Bargaining Problem," Econometrica, Econometrica, vol. 18 (1950), pp. 15562. vol. 18 (1950), pp. 15562.

2. Nash's bargaining solution was "virtually unantic.i.p.ated in the literature," according to Roger B. Myerson, "John Nash's Contribution to Economics," Games and Economic Behavior, Games and Economic Behavior, no. 14 (1996), p. 291. See also Ariel Rubinstein, "John Nash: The Master of Economic Modeling," no. 14 (1996), p. 291. See also Ariel Rubinstein, "John Nash: The Master of Economic Modeling," The Scandinavian Journal of Economics, The Scandinavian Journal of Economics, vol. 97, no. 1 (1995), pp. 1112; John C. Harsanyi, "Bargaining," in Eatwell, Milgate, and Newman, op. cit., pp. 5660; Andrew Schotter, interview, 10.25.96; Ariel Rubinstein, interview, 11.25.96; James W. Friedman, professor of economics, University of North Carolina, interview, 10.2.96. vol. 97, no. 1 (1995), pp. 1112; John C. Harsanyi, "Bargaining," in Eatwell, Milgate, and Newman, op. cit., pp. 5660; Andrew Schotter, interview, 10.25.96; Ariel Rubinstein, interview, 11.25.96; James W. Friedman, professor of economics, University of North Carolina, interview, 10.2.96.

3. "This is the cla.s.sical problem of exchange and, more specifically, of bilateral monopoly as treated by Cournot, Bowley, Tintner, Fellner and others," Nash, "The Bargaining Problem," p. 155. As Harold Kuhn points out, Nash's delineation of the history of the problem was undoubtedly supplied by Oskar Morgenstern, "It is now clear that Nash had not read those writers," Harold Kuhn, "n.o.bel Seminar," Les Prix n.o.bel 1994. Les Prix n.o.bel 1994. For a delightful short history of exchange, including the references to pharaohs and kings, see Robert L. Heilbroner, For a delightful short history of exchange, including the references to pharaohs and kings, see Robert L. Heilbroner, The Worldly Philosophers, The Worldly Philosophers, 6th edition (New York: Touchstone, 1992), p. 27. 6th edition (New York: Touchstone, 1992), p. 27.

4. John C. Harsanyi, "Approaches to the Bargaining Problem Before and After the Theory of Games: A Critical Discussion of Zeuthen's, Hick's and Nash's Theories," Econometrica, Econometrica, vol. 24 (1956), pp. 14457. vol. 24 (1956), pp. 14457.

5. In his now-cla.s.sic reformulation of the Nash bargaining model, Ariel Rubinstein traces the bargaining problem to Edgeworth, "Mathematical Psychics: An Essay on the Application of MatKematics to the Moral Sciences" (London: C. Kegan Paul, 1881), reprinted in Mathematical Psychics and Other Essays Mathematical Psychics and Other Essays (Mountain Center, Calif.: James & Gordon, 1995). Martin Shubik writes, "Even as a graduate student I was struck by the contrast between cooperative game theory, the seeds of which I regarded as already present in Edgeworth and noncooperative theory which was present in Cournot," Martin Shubik, (Mountain Center, Calif.: James & Gordon, 1995). Martin Shubik writes, "Even as a graduate student I was struck by the contrast between cooperative game theory, the seeds of which I regarded as already present in Edgeworth and noncooperative theory which was present in Cournot," Martin Shubik, Collected Works, Collected Works, forthcoming, p. 6. For lively accounts of Edgeworth's life and contributions, see Heilbroner, op. cit., pp. 17476, and John Maynard Keynes, "Obituary of Francis Isidro Edgeworth, March 26, 1926," reprinted in Edgeworth, op. cit. forthcoming, p. 6. For lively accounts of Edgeworth's life and contributions, see Heilbroner, op. cit., pp. 17476, and John Maynard Keynes, "Obituary of Francis Isidro Edgeworth, March 26, 1926," reprinted in Edgeworth, op. cit.

6. Fleilbroner, op. cit., p. 173.

7. Ibid., p. 174.

8. Edgeworth, op. cit.

9. Ibid.

10. Ibid.

11. Harsanyi, op. cit.

12. John von Neumann and Oskar Morgenstern, The Theory of Games and Economic Behavior, The Theory of Games and Economic Behavior, op. cit., p. 9. "It may also be regarded as a nonzero-sum two-person game," Nash, "The Bargaining Problem," op. cit., p. 155; "even though von Neumann and Morgenstern's theory of games was an essential step toward a strong bargaining theory, their own a.n.a.lysis of two-person bargaining games did not go significantly beyond the weak bargaining theory of neocla.s.sical economics," Harsanyi, "Bargaining," op. cit., pp. 5657. op. cit., p. 9. "It may also be regarded as a nonzero-sum two-person game," Nash, "The Bargaining Problem," op. cit., p. 155; "even though von Neumann and Morgenstern's theory of games was an essential step toward a strong bargaining theory, their own a.n.a.lysis of two-person bargaining games did not go significantly beyond the weak bargaining theory of neocla.s.sical economics," Harsanyi, "Bargaining," op. cit., pp. 5657.

13. See, for example, Robert J. Leonard, "From Parlor Games to Social Science," op. cit., for a history of the axiomatic approach, and a superb interpretive discussion of "axiomatics" in Robert J. Aumann, "Game Theory," in John Eatwell, Murray Milgate, and Peter Newman, The New Palgrave, The New Palgrave, op. cit., pp. 2628. op. cit., pp. 2628.

14. Von Neumann and Morgenstern used the axiomatic method to derive their theory of expected or von Neumann-Morgenstern utilities in the second, 1947, edition of The Theory of Games and Economic Behavior. The Theory of Games and Economic Behavior. The first application to a problem in social sciences, I believe, was Kenneth J. Arrow's Ph.D. thesis The first application to a problem in social sciences, I believe, was Kenneth J. Arrow's Ph.D. thesis Social Choice and Individual Values Social Choice and Individual Values (New York: John Wiley & Sons, 1951). Lloyd S. Shapley's "A Value of N-Person Games," (New York: John Wiley & Sons, 1951). Lloyd S. Shapley's "A Value of N-Person Games," Contributions to the Theory of Games II Contributions to the Theory of Games II (Princeton: Princeton University Press, 1953), pp. 30717, is another stellar example. (Princeton: Princeton University Press, 1953), pp. 30717, is another stellar example.

15. John Nash, "The Bargaining Problem," op. cit., p. 155.

16. John Nash, Les Prix n.o.bel 1994, Les Prix n.o.bel 1994, op. cit., pp. 27677. op. cit., pp. 27677.

17. The sketch of Bart Hoselitz is based on an interview with his friend Sherman Robinson, professor of economics, University of Chicago, 7.95, and questionnaires, letters, and a curriculum vitae from Carnegie-Mellon University archives.

18. This bit of history about international trade theory after World War II was supplied by Kenneth Rogoff, professor of economics, Princeton University, interview.

19. John Nash, Les Prix n.o.bel 1994, Les Prix n.o.bel 1994, op. cit., pp. 17677. op. cit., pp. 17677.

20. Nash told Myerson that he was inspired by a problem posed by Hoselitz. Roger Myerson, professor of economics, Northwestern University', interview, 8.7.97.

21. Myerson, e-mail, 8.11.97.

22. Letter from John Nash to Martin Shubik, undated (written in 1950 or 1951).

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, 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. 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 n.o.bel 1994, Les Prix n.o.bel 1994, op. cit., p. 277. 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 Poincare, quoted in E. T. Bell, Men of Mathematics, Men of Mathematics, op. cit., p. 551. 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, John von Neumann, op. cit., pp. 35056. op. cit., pp. 35056.

13. As told to Harold Kuhn, 4.17.97.

14. John Nash, Les Prix n.o.bel 1994, Les Prix n.o.bel 1994, op. cit. op. cit.

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

19. John F. Nash, Jr., "Equilibrium Points in N-Person Games," communicated by S. Lefschetz, 11.16.49, pp. 4849.

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 Two Year College Mathematics Journal vol. 14, no. 3 (June 1983). vol. 14, no. 3 (June 1983).

24. Tucker, interview.

25. Harold Kuhn, "n.o.bel Seminar," Les Prix n.o.bel 1994, Les Prix n.o.bel 1994, op. cit., p. 283. op. cit., p. 283.