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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Stochastic equilibria in von Neumann-Gale dynamical systems


Authors: Igor V. Evstigneev and Klaus Reiner Schenk-Hoppé
Journal: Trans. Amer. Math. Soc. 360 (2008), 3345-3364
MSC (2000): Primary 37H99, 37H15; Secondary 91B62, 91B28.
Published electronically: January 11, 2008
MathSciNet review: 2379800
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Abstract | References | Similar Articles | Additional Information

Abstract: This paper examines a class of random dynamical systems related to the classical von Neumann and Gale models of economic dynamics. Such systems are defined in terms of multivalued operators in spaces of random vectors, possessing certain properties of convexity and homogeneity. We establish a general existence theorem for equilibrium, which holds under conditions analogous to the standard deterministic ones. Our results answer questions that remained open for more than three decades.


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Additional Information

Igor V. Evstigneev
Affiliation: Economics Department, University of Manchester, Oxford Road, Manchester, M13 9PL, United Kingdom
Email: igor.evstigneev@manchester.ac.uk

Klaus Reiner Schenk-Hoppé
Affiliation: School of Mathematics and Leeds University Business School, Leeds University, Leeds LS2 9JT, United Kingdom
Email: K.R.Schenk-Hoppe@leeds.ac.uk

DOI: http://dx.doi.org/10.1090/S0002-9947-08-04445-0
PII: S 0002-9947(08)04445-0
Keywords: Random dynamical systems, convex multivalued operators, von Neumann--Gale model, rapid paths, convex duality, stochastic equilibrium
Received by editor(s): July 5, 2006
Received by editor(s) in revised form: October 27, 2006
Published electronically: January 11, 2008
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.