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Debreu, Gerard

A social equilibrium existence theorem. (English) Zbl 0047.38804

Proc. Natl. Acad. Sci. USA 38, 886-893 (1952).
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Cited in 5 Reviews
Cited in 354 Documents

Keywords:

mathematical biology, operations research
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References:

[1] Aronszajn, N., and Borsuk, K., ”Sur la somme et le produit combinatoire des rétractes absolus,” Fundamenta Mathematicae, 18, 193–197 (1932) · Zbl 0004.22603
[2] Arrow, K. J., and Debreu, G., ”Existence of an Equilibrium for a Competitive Economy,” Econometrica, in press (1953) · Zbl 0055.38007
[3] Begle, E. G., ”A Fixed Point Theorem,” Ann. Math., 51, No. 3, 544–550 (May, 1950) · Zbl 0036.38901 · doi:10.2307/1969367
[4] Borsuk, K., ”Über eine Klasse von lokal zusammenhängenden Räumen,” Fundamenta Mathematicae, Vol. 19 (1932), p. 220–242 · JFM 58.0629.02
[5] Bourbaki, N., Eléments de Mathématique, Première partie, Livre III, Chap. IV, §4, Hermann, Paris, 1942
[6] Eilenberg, S., and Montgomery, D., ”Fixed Point Theorems for Multi-valued Transformations,” Am. J. Math., 68, 214–222 (1946) · Zbl 0060.40203 · doi:10.2307/2371832
[7] Kakutani, S., ”A Generalization of Brouwer’s Fixed Point Theorem,” Duke Math. J., 8, No. 3, 457–459 (September, 1941) · JFM 67.0742.03 · doi:10.1215/S0012-7094-41-00838-4
[8] Nash, John F., ”Equilibrium Points in N-Person Games,” Proc. Natl. Acad. Sci. 36, 48–49 (1950) · Zbl 0036.01104 · doi:10.1073/pnas.36.1.48
[9] Neumann, J. von, ”Zur Theorie der Gesellschaftsspiele,” Math. Ann., 100, 295–320 (1928) · JFM 54.0543.02 · doi:10.1007/BF01448847
[10] Neumann, J. von, ”Über ein ökonomisches Gleichungssystem und eine Verallgemeinerung des Brouwerschen Fixpunktsatzes,” Ergebnisse eines Mathematischen Kolloquiums, 8, 73–83 (1937), (translated in Rev. Economic Studies, XIII, No. 33, 1–9 (1945–46) · Zbl 0017.03901
[11] Neumann, J. von, and Morgenstem, O., Theory of Games and Economic Behavior, 2nd ed., Princeton University Press, Princeton, 1947 (1st ed., 1944)
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