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Mathematical Systems Theory and Economics I / II pp 337–346Cite as

The Core and Competitive Equilibria

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Part of the book series: Lecture Notes in Operations Research and Mathematical Economics ((LNE,volume 11/12))

Abstract

There is at least a formal connection between Control Theory and Mathematical Economics. Some recent important results in equilibrium analysis of perfectly competitive economies (i.e., economies with an atomless measure space of economic agents) are based on mathematical theorems which are equally basic mathematical tools in Control Theory.

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References

  1. Aumann, R. J., Markets with a Continuum of Traders. Econometrica, 32, 39–50 (1964).

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  2. Aumann, R. J., Existence of Competitive Equilibria in Markets with a Continuum of Traders. Econometrica, 34, 1–17 (1966).

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  3. Aumann, R. J., Measurable Utility and Measurable Choice Theorem. (To appear in: Proceedings of the Colloque International du Centre National de la Recherche Scientifique “La Decision”, Aix-en-Provence, 3-7 Juillet 1967).

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  4. Debreu, G., Theory of Value. New York, Wiley (1959).

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  5. Hildenbrand, W., The Core of an Economy with a Measure Space of Economic Agents. (To appear in The Review of Economic Studies, Oct. 1968).

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  6. Liapunov, A., Sur les Fonctions-vecteurs Completement Additives. Bull. Acad. Sci. URSS, Ser. Math., 4, 465–478 (1940).

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  7. Von Neumann, J., On Rings of Operators, Reduction Theory. Ann. Math., 50, 401–485 (1949).

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  8. Sion, M., On Uniformization of Sets in Topological Spaces. Trans. Am. Math. Soc, 96, 237–246 (1960).

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  9. Vind, K., Edgeworth-Allocations in an Exchange Economy with Many Traders. International Economic Review, 5, 165–177 (1964).

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Authors
  1. Werner Hildenbrand
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Editor information

Editors and Affiliations

  1. Princeton University, Princeton, N. J., USA

    H. W. Kuhn

  2. University of Milano, Milano, ltaly

    G. P. Szegö

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© 1969 Springer-Verlag Berlin Heidelberg

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Hildenbrand, W. (1969). The Core and Competitive Equilibria. In: Kuhn, H.W., Szegö, G.P. (eds) Mathematical Systems Theory and Economics I / II. Lecture Notes in Operations Research and Mathematical Economics, vol 11/12. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-46196-5_17

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  • DOI: https://doi.org/10.1007/978-3-642-46196-5_17

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-04635-6

  • Online ISBN: 978-3-642-46196-5

  • eBook Packages: Springer Book Archive

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