Game Theory pp 242-252 | Cite as

John von Neumann

  • Gerald L. Thompson
Part of the The New Palgrave book series

Abstract

his life. Jansci (John) von Neumann was born to Max and Margaret Neumann on 28 December 1903 in Budapest, Hungary. He showed an early talent for mental calculation, reading and languages. In 1914, at the age of ten, he entered the Lutheran Gymnasium for boys. Although his great intellectual (especially mathematical) abilities were recognized early, he never skipped a grade and instead stayed with his peers. An early teacher, Laslo Ratz, recommended that he be given advanced mathematics tutoring, and a young mathematician Michael Fekete was employed for this purpose. One of the results of these lessons was von Neumann’s first mathematical publication (joint with Fekete) when he was 18.

Keywords

Assure Keystone 

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Selected Works

  1. 1928.
    Zur Theorie der Gesellschaftsspiele. Mathematische Annalen 100, 295–320.Google Scholar
  2. 1937.
    Über ein ökonomisches Gleichungssystem und eine Verallgemeinerung des Brouwerschen Fixpunktsatzes. Ergebnisse eines Mathematische Kolloquiums 8, ed. Karl Menger. Trans. as ‘A model of general equilibrium’, Review of Economic Studies 13, (1945–6), 1–9.Google Scholar
  3. 1944.
    (With O. Morgenstern.) Theory of Games and Economic Behavior. Princeton: Princeton University Press. 2nd edn, 1947; 3rd edn, 1953.Google Scholar
  4. 1947.
    Discussion of a maximum problem. Unpublished working paper, Princeton, November, 9 pp.Google Scholar
  5. 1948.
    A numerical method for determining the value and the best strategies of a zero-sum two-person game with large numbers of strategies. Mimeographed, May, 23 pp.Google Scholar
  6. 1953.
    Communications on the Borel notes. Econometrica 21, 124–5.Google Scholar
  7. 1953b.
    (With G.W. Brown.) Solutions of games by differential equations. In Contributions to the Theory of Games Vol. 1, ed. H.W. Kuhn and A.W. Tucker, Annals of Mathematics Studies No. 28, Princeton: Princeton University Press.Google Scholar
  8. 1953c.
    (With D.B. Gillies and J.P. Mayberry.) Two variants of poker. In Contributions to the Theory of Games Vol. 1, ed. H.W. Kuhn and A.W. Tucker, Annals of Mathematics Studies No. 28, Princeton: Princeton University Press.Google Scholar
  9. 1954.
    A numerical method to determine optimum strategy. Naval Research Logistics Quarterly 1, 109–15.Google Scholar
  10. 1958.
    The Computer and the Brain. New Haven: Yale University Press.Google Scholar
  11. 1963.
    Collected Works Vols I—VI. New York: Macmillan.Google Scholar

Bibliography

  1. Champernowne, D.G. 1945–6. A note on J. von Neumann’s article. Review of Economic Studies 13, 10–18.CrossRefGoogle Scholar
  2. Debreu, G. 1959. Theory of Value: an axiomatic analysis of economic equilibrium. Cowles Foundation Monograph No. 17, New York: Wiley.Google Scholar
  3. Gale, D. 1956. The closed linear model of production. In Linear Inequalities and Related Systems, ed. H.W. Kuhn and A.W. Tucker, Princeton: Princeton University Press. A counter-example showing that optimal prices need not exist in Gale’s original model was published by J. Hulsman and V. Steinmitz in Econometrica 40, (1972), 387–90. Proof of the existence of optimal prices in a modified Gale model was given by A. Soyster in Econometrica 42, (1974), 199–205.Google Scholar
  4. Goldstine, H.H. 1972. The Computer from Pascal to von Neumann. Cambridge, Mass.: MIT Press.Google Scholar
  5. Heims, S.J. 1980. John von Neumann and Norbet Wiener. Cambridge, Mass.: MIT Press.Google Scholar
  6. Kemeny, J.G., Morgenstern, O. and Thompson, G.L. 1956. A generalization of von Neumann’s model of an expanding economy. Econometrica 24, 115–35.CrossRefGoogle Scholar
  7. Los, J. 1974. The existence of equilibrium in an open expanding economy model (generalization of the Morgenstern-Thompson model). In Mathematical Models in Economics, ed. J. and M.W. Los, Amsterdam and New York: North-Holland Publishing Co.Google Scholar
  8. Lucas, W. 1969. The proof that a game may not have a solution. Transactions of the American Mathematical Society 137, 219–29.CrossRefGoogle Scholar
  9. Luce, R.D. and Raiffa, H. 1957. Games and Decisions: Introduction and Critical Survey. New York: John Wiley & Sons.Google Scholar
  10. Moeschlin, O. 1974. A generalization of the open expanding economy model. Econometrica 45, 1767–76.CrossRefGoogle Scholar
  11. Morgenstern, O. 1958. Obituary, John von Neumann, 1903–57. Economic Journal 68, 170–74.Google Scholar
  12. Morgenstern, O. 1976. The collaboration between Oskar Morgenstern and John von Neumann on the theory of games. Journal of Economic Literature 14, 805–16.Google Scholar
  13. Morgenstern, O. and Thompson, G.L. 1969. An open expanding economy model. Naval Research Logistics Quarterly 16, 443–57.CrossRefGoogle Scholar
  14. Morgenstern, O. and Thompson, G.L. 1976. Mathematical Theory of Expanding and Contracting Economies. Boston: Heath-Lexington.Google Scholar
  15. Oxtoby, J.C., Pettis, B.J. and Price, G.B. (eds) 1958. John von Neumann 1903–1957. Bulletin of the American Mathematical Society 64(3), Part 2.Google Scholar
  16. Shapley, L.S. 1953. A value for n-person games. In Contributions to the Theory of Games II, ed. H.W. Kuhn and A.W. Tucker, Princeton: Princeton University Press.Google Scholar
  17. Shapley, L.S. and Shubik, M. 1972. The assignment game. I: the core. International Journal of Game Theory 1, 111–30.CrossRefGoogle Scholar
  18. Shubik, M. 1982. Game Theory in the Social Sciences: Concepts and Solutions. Cambridge, Mass.: MIT Press.Google Scholar
  19. Shubik, M. 1985. A Game Theoretic Approach to Political Economy. Cambridge, Mass.: MIT Press.Google Scholar
  20. Thompson, G.L. 1956. On the solution of a game-theoretic problem. In Linear Inequalities and Related Systems, ed. H.W. Kuhn and A.W. Tucker, Princeton: Princeton University Press.Google Scholar
  21. Thompson, G.L. 1980. Computing the core of a market game. In External Methods and Systems Analysis, ed. A.V. Fiacco and K.O. Kortanek, Berlin: Springer-Verlag.Google Scholar
  22. Thompson, G.J. 1981. Auctions and market games. In Essays in Game Theory and Mathematical Economics in Honor of Oskar Morgenstern, ed. R.J. Aumann et al., Mannheim: Bibliographisches Institut Mannheim.Google Scholar
  23. Wald, A. 1935. Uber die eindeutige positive Losbarkeit der neuen Produktionsgleichungen. Ergebnisse eines mathematischen Kolloquiums, ed. K. Menger 6, 12–20.Google Scholar

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© Palgrave Macmillan, a division of Macmillan Publishers Limited 1989

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  • Gerald L. Thompson

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