Abstract
A possible way to show the existence of solutions to a generalized von Neumann growth model, due to Kemeny, Morgenstern and Thompson leads to a discussion of a game value function ∅: R+ → R,
where Mα: B -αA; B, A being nonnegative matrices of order m×n, α∈ R+;
Abstract of a paper presented to the Symposium on von Neumann Models, organized by the Institute of Mathematics of the Polish Academy of Sciences, held in Warsaw, July, 10-15, 1972, and subsequently to the Jahrestagung der Deutschen Gesellschaft für Operations Research, Hamburg, Sept., 6-8, 1972. The research described in this paper was carried out under grants from the Deutsche Forschungsgemeinschaft.
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Literatur
J.G. Kemeny, O. Morgenstern and G.L. Thompson: A Generalization of the von Neumann-Model of an Expanding Economy, Econometrica 1956, pp. 115–135.
H.D. Mills: Marginal Values of Matrix Games and Linear Programs, in Linear Inequalities and Related Systems (Editors: H.W. Kuhn and A.W. Tucher), Princeton, New Jersey, 1956, pp. 183–198.
O. Morgenstern and G.L. Thompson: An Open Expanding Economy Model, Noval Research Logistics Quarterly 16, 1969, pp. 443–457.
G.L. Thompson: On the Solution of a Game Theoretic Problem, in Linear Inequalities and Related Systems (Editors: H.W. Kuhn and A.W. Tucher), Princeton, New Jersey, 1956, pp. 275–284.
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© 1973 Physica-Verlag, Rudolf Leibing KG, Würzburg
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Moeschlin, O. (1973). Derivatives of a Game Value Function in Connection with von Neumann Growth Models. In: Jacob, H., Pressmar, D.B., Todt, H., Zimmermann, HJ. (eds) Vorträge der Jahrestagung 1972 DGOR / Papers of the Annual Meeting 1972. Proceedings in Operations Research, vol 1972. Physica-Verlag HD. https://doi.org/10.1007/978-3-642-99746-4_7
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DOI: https://doi.org/10.1007/978-3-642-99746-4_7
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