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Search Results for fixed-point theorem
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History of Political Economy (2016) 48 (4): 635–655.
Published: 01 December 2016
... 2016 fixed-point theorem general equilibrium theory Vienna Mathematical Colloquium Karl Menger Abraham Wald References Arrow Kenneth J. Debreu Gérard . 1954 . “Existence of an Equilibrium for a Competitive Economy.” Econometrica 22 ( 3 ): 265 – 90 . Arrow...
History of Political Economy (2006) 38 (Suppl_1): 213–227.
Published: 01 December 2006
... Equilibria. New Haven, Conn.: Yale University Press. Sonnenschein, H. 1973 . Do Walras' Identity and Continuity Characterize the Class of Community Excess Demand Functions? Journal of Economic Theory 6 : 345 -54. Uzawa, H. 1962 . Walras' Existence Theorem and Brouwer's Fixed Point Theorem...
History of Political Economy (1991) 23 (3): 560–565.
Published: 01 September 1991
... in turn. First is Von Neumann’s approach, using convex analysis, fixed point theorems, and game theory (257). Second is the line of inquiry that began with Wald’s work and led to a blind alley in the work of Kenneth J. Arrow and Frank H. Hahn (258). It is strange to read the authors...
History of Political Economy (2022) 54 (5): 823–858.
Published: 01 October 2022
... with Brouwer's fixed point theorem; that proof was later simplified by Kakutani. I have now found a much simpler proof based on the theorem of “supporting planes” of convex bodies—and I think that I see now a connection between these questions and the theory of convex bodies, which might be of some interest. 14...
History of Political Economy (1990) 22 (1): 101–112.
Published: 01 March 1990
... and Political Science. Kakutani , S. 1941 . A generalization of Brouwer's fixed point theorem. Duke Mathematical Journal 8 : 457 -59. Koopmans , T. C. 1951a . Analysis of production as an efficient combination of activities. In Activity analysis of production and allocation , 33 -97...
History of Political Economy (2004) 36 (4): 639–666.
Published: 01 November 2004
... with convex images, it is possible to apply Kakutani ﬁxed-point theorem to prove that the mapping has a ﬁxed point, which is the desired equilib- rium. Hence Nash proves that every n-player ﬁnite game played with mixed strategies admits an equilibrium point. Moreover, for the ﬁrst time in game theory he...
History of Political Economy (2020) 52 (4): 799–801.
Published: 01 August 2020
... of Japanese mathematicians such as Shizuo Kakutani s 800 Book Reviews fixed-point theorem). It is striking to learn that as early as 1939 Kazuo Midutani pub- lished in Japanese Comments on Wald s Proof of the Existence of Equilibrium for the Cassel-Schlesinger System of Production (reprinted in his...
History of Political Economy (1975) 7 (4): 530–548.
Published: 01 November 1975
.... Arrow and L. Hurwicz, “On the Stability of a Competitive Equilibrium, I,” Econometrica, Oct. 1958. 34. The major tool used to solve the existence problem, a fixed point theorem, was developed in 1941 by S. Kakutani, “A Generalization of Brouwer’s Fixed Point Theorem,” Duke Mathematical...
History of Political Economy (1995) 27 (1): 195–199.
Published: 01 March 1995
... is the most consistent path to human dignity. I find it troubling to think that we should ever lose sight of Marx’s work. Historians of economics should not restrict themselves to a story of analytical progress. The economy does not present itself in terms of fixed point theorems or quasi...
History of Political Economy (2021) 53 (4): 595–631.
Published: 01 August 2021
... to the (structural) parameters of his system, von Neumann offered an analytical treatment. Incidentally, when calculating the roots of the system, von Neumann used a Brouwer s fixed-point theorem. With it, he concluded, There are infinitely many solutions in existence. 51 These notes clearly instantiated...
History of Political Economy (2002) 34 (2): 291–320.
Published: 01 June 2002
...” by Benoit Mandelbrot. Information and Control 4 : 217 -23. ____. 1979 . Rational Decision Making in Business Organizations. American Economic Review 69.4 : 493 -513. ____. 1982a . Accurate Predictions and Fixed Point Theorems: Comments. Social Science Information 21.4-5 : 605 -26...
History of Political Economy (1972) 4 (2): 533–550.
Published: 01 June 1972
... of a ked point which was his generabtion land a more applicable fomdation of Brouwer’s theorem. He wrote an article on this theorerm, “A Generalization of Brouwer’s Fixed Point ‘Theorem” in 19413O from a mathematical point of view, because he is a math- mabician. I know that in 1935-36 von...
History of Political Economy (1992) 24 (Supplement): 15–27.
Published: 01 December 1992
... Neumann sent Borel a note on his result, which Borel presented to the Academie des Sciences in June 1928. In his 1937 paper, von Neumann gave an entirely topological proof of the existence of general competitive equilibrium, using Brouwer’s fixed- point theorem to provide a much clearer...
History of Political Economy (2020) 52 (5): 863–894.
Published: 01 October 2020
... questions depend on one another, and the solution had to use a fixed-point theorem. He assumed, for simplicity, constant returns to scale and supposed an economy that could expand but with an unchanged structure: each of the possible production processes would be used in cer- tain intensities...
History of Political Economy (1975) 7 (2): 174–192.
Published: 01 June 1975
... commentary on the theorem, more than a half-century later, was a composite of Jevons’ and Marshall’s. Like the former, he pointed out that capital consisted of nothing more than advances. Then, altering the latter’s analysis slightly, he noted that the only real difference between the two...
History of Political Economy (1999) 31 (3): 511–523.
Published: 01 September 1999
... constant or decreasing returns describe the economy in operation? At this point, we must distinguish categorically between generalized increasing returns and alternative models, as sketched out in section 1. If increasing returns are present for productive activities that are iden- tified...
History of Political Economy (1991) 23 (1): 167–170.
Published: 01 March 1991
.... As one might expect, the central purpose of the book is to develop and support Hollander’s one-paradigm interpretation of the history of economic thought. Two points capture the general thrust of his thesis: 1. There is a core of general equilibrium economics accounting for re...
History of Political Economy (2007) 39 (Suppl_1): 76–95.
Published: 01 December 2007
... René Roy. The Brouwer fixed-point theorem and the Kakutani fixed-point theorem are so named not just to honor those who first stated them but also to make it easier to recall which is which. Long lists of names and subtle distinctions among individual contribu- tions and points of view...
History of Political Economy (2004) 36 (1): 103–129.
Published: 01 March 2004
... the minimum Schmidt / Early Use of the Envelope Theorem 123 points of the short-run average cost curves, Harrod’s ﬁrst graph of this type from the same year (1931, 575) is correct, showingshort-run and long-run average costs of production for the case of increasing returns to scale...
History of Political Economy (1998) 30 (4): 571–599.
Published: 01 November 1998
...- structions of Malthus’s growth theory r is invariant with respect to N. Moreover the “extraordinary improvements in the modes of cultiva- tion” which Malthus thought might subvert his theorem are beside the point (W 7: 130). For with any formulation of the diminishing-returns production function...