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John von Neumann's work in the theory of games and mathematical economics
Author(s):
H. W.
Kuhn;
A. W.
Tucker
Journal:
Bull. Amer. Math. Soc.
64
(1958),
Part 2:100-122.
MathSciNet review:
0096572
Retrieve article in:
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Additional information
References:
- A. John von Neumann, Zur Theorie der Gesellschaftsspiele, Math. Ann. vol. 100 (1928) pp. 295-320. MR 1512486
- B. John von Neumann, Über ein ökonomisches Gleichungssystem und eine Verallgemeinerung des Brouwerschen Fixpunktsatzes, Ergeb. eines Math. Koll. Vienna (ed. by Karl Menger) vol. 8 (1937) pp. 73-83.
- C. John von Neumann, A model of general economic equilibrium, Rev. Economic Studies vol. 13 (1945-1946) pp. 1-9 (Translation of [B]).
- D. John von Neumann, Theory of games and economic behavior (with Oskar Morgenstern) 1st ed., Princeton, 1944, 625 pp.; 2d ed., Princeton, 1947, 641 pp.; 3d ed., Princeton, 1953, 641 pp. MR 21298
- E. John von Neumann, Discussion of a maximum problem (unpublished working paper, Princeton, November, 1947, 9 pp.).
- F. John von Neumann, A numerical method for determination of the value and the best strategies of a zero-sum two-person game with large numbers of strategies, mimeographed, Princeton, May 1948, 23 pp.
- G. John von Neumann, Solutions of games by differential equations (with G. W. Brown), Contributions to the Theory of Games, vol. I (ed. by H. W. Kuhn and A. W. Tucker) Ann. of Math. Studies, no. 24, Princeton, 1950, pp. 73-79. MR 39220
- H. John von Neumann, A certain zero-sum two-person game equivalent to the optimal assignment problem, Contributions to the Theory of Games, vol. II (ed. by H. W. Kuhn and A. W. Tucker) Ann. of Math. Studies, no. 28, Princeton 1953, pp. 5-12. MR 54920
- I. John von Neumann, Two variants of poker (with D. B. Gillies and J. P. Mayberry), ibid. pp. 13-50. MR 54925
- J. John von Neumann, Communication on the Borel notes, Econometrica vol. 21 (1953) pp. 124-125. MR 52755
- K. John von Neumann, A numerical method to determine optimum strategy, Nav. Res. Logist. Quart. vol. 1 (1954) pp. 109-115. MR 63776
- 1.
- K. J. Arrow, Alternative approaches to the theory of choice in risk-taking situations, Econometrica vol. 19 (1951) pp. 404-437; Utilities, attitudes, choices: A review note, ibid. vol. 26 (1958) pp. 1-23. MR 46020
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- 4.
- M. Dresher, A. W. Tucker, and P. Wolfe (editors), Contributions to the Theory of Games, vol. III, Ann. of Math. Studies, no. 39, Princeton, 1957.
- 5.
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- 6.
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- 7.
- S. Kakutani, A generalization of Brouwer's fixed point theorem, Duke Math. J. vol. 8 (1941) pp. 457-459. MR 4776
- 8.
- L. Kalmar, Zur Theorie der abstrakten Spiele, Acta Sci. Math. Szeged. vol. 4 (1928-1929) pp. 65-85.
- 9.
- J. G. Kemeny, O. Morgenstern and G. L. Thompson, A generalization of the von Neumann model of an expanding economy, Econometrica vol. 24 (1956) pp. 115-135. MR 80573
- 10.
- H. Kneser, Sur un théorème fondamental de la théorie des jeux, C. R. Acad. Sci. Paris vol. 234 (1952) pp. 2418-2420. MR 50249
- 11.
- D. König, Über eine Schlussweise aus dem Endlichen ins Unendliche, Acta Sci. Math. Szeged. vol. 3 (1927) pp. 121-130.
- 12.
- T. C. Koopmans (editor), Activity analysis of production and allocation, Cowles Commission Monograph, no. 13, New York, 1951.
- 13.
- H. W. Kuhn and A. W. Tucker, Nonlinear programming, Proceedings of the Second Berkeley Symposium on Mathematical Statistics and Probability (J. Neyman, ed.), Berkeley, 1951, pp. 481-492. MR 47303
- 14.
- H. W. Kuhn and A. W. Tucker (editors), Contributions to the theory of games, vol. I, Ann. of Math. Studies, no. 24, Princeton, 1950.
- 15.
- H. W. Kuhn and A. W. Tucker (editors), Contributions to the theory of games, vol. II, Ann. of Math. Studies, no. 28, Princeton, 1953.
- 16.
- H. W. Kuhn and A. W. Tucker (editors), Linear inequalities and related systems, Ann. of Math Studies, no. 38, Princeton, 1956.
- 17.
- R. D. Luce and H. Raiffa, Games and decisions, New York, 1957.
- 18.
- R. D. Luce and A. W. Tucker (editors), Contributions to the theory of games, vol. IV, Ann. of Math. Studies, no. 40, Princeton (in press).
- 19.
- J. McDonald, Strategy in poker, business, and war, New York, 1950.
- 20.
- J. F. Nash, Non-cooperative games, Ann. of Math. vol. 54 (1951) pp. 286-295. MR 43432
- 21.
- R. Otter and J. J. Dunne, Games with equilibrium points, Proc. Nat. Acad. Sci. U.S.A. vol. 39 (1953) pp. 310-314. MR 54228
- 22.
- F. P. Ramsey, Truth and probability (1926), Further considerations (1928), Foundations of Mathematics and Other Logical Essays, London and New York, 1931.
- 23.
- M. Richardson, On weakly ordered systems, Bull. Amer. Math. Soc. vol. 52 (1946) pp. 113-116; Extension theorems for solutions of irreflexive relations, Proc. Nat. Acad. Sci. U.S.A. vol. 39 (1953) pp. 649-655; Solutions of irreflexive relations, Ann. of Math. vol. 58 (1953) pp. 573-590; Relativization and extension of solutions of irreflexive relations, Pacific J. Math. vol. 5 (1955) pp. 551-584. MR 86752
- 24.
- L. J. Savage, The foundations of statistics, New York, 1954. MR 63582
- 25.
- L. S. Shapley, Stochastic games, Proc. Nat. Acad. Sci. U.S.A. vol. 39 (1953) pp. 1095-1100. MR 61807
- 26.
- J. Ville, Sur la théorie générale des jeux où intervient l'habileté des joueurs, Traité du Calcul des Probabilités et de ses Applications (by É. Borel and collaborators) vol. IV, no. 2, Paris, 1938, pp. 105-113.
- 27.
- A. Wald, Über die eindeutige positive Lösbarkeit der neuen Produktionsgleichungen, Ergeb. eines Math. Koll. Vienna (ed. by Karl Menger) vol. 6 (1935) pp. 12-20; Über die Produktionsgleichungen der ökonomischen Wertlehre, ibid. vol. 7 (1936) pp. 1-6; Über einige Gleichungssysteme der mathematischen Ökonomie, Z. National-ökonomie vol. 7 (1936) pp. 637-670 [English translation in Econometrica vol. 19 (1951) pp. 368-403].
- 28.
- A. Wald, Generalization of a theorem by v. Neumann concerning zero sum two person games, Ann. of Math. vol. 46 (1945) pp. 281-286; Statistical decision functions which minimize the maximum risk, ibid. pp. 265-280; Statistical decision functions, New York, 1950. MR 11938
- 29.
- P. Wolfe, The strict determinateness of certain infinite games, Pacific J. Math. vol. 5 (1955) pp. 841-847. MR 73909
- 30.
- E. Zermelo, Über eine Anwendung der Mengenlehre auf die Theorie des Schachspiels, Proceedings of the Fifth International Congress of Mathematicians, Cambridge, 1912, vol. 2, p. 501-504.
Additional Information:
DOI:
10.1090/S0002-9904-1958-10209-8
PII:
S 0002-9904(1958)10209-8
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