Continuous Approximation of Dynamical Systems with Randomly Matched Individuals

Biologists and economists have analyzed populations in which each individual interacts with randomly selected individuals. Because random matching generates a very complicated stochastic process, biologists and economists frequently approximate the population dynamics by a deterministic process. Thi...

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Bibliographic Details
Published in:Journal of economic theory 1995-08, Vol.66 (2), p.615-625
Main Author: Boylan, Richard T.
Format: Article
Language:English
Subjects:
Dynamics
Economic theory
Individuals
Population
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Summary:Biologists and economists have analyzed populations in which each individual interacts with randomly selected individuals. Because random matching generates a very complicated stochastic process, biologists and economists frequently approximate the population dynamics by a deterministic process. This paper examines the limit of random matching schemes as the population grows, matches occur very frequently, and the proportion of the population paired in a matching becomes very small. In the limit, the population evolves according to a differential equation. The proof of convergence depends either on the existence of a global attractor or an finiteness of the time horizon. Journal of Economic Literature Classification Numbers: C73, C78, D83.
ISSN:0022-0531
1095-7235
DOI:10.1006/jeth.1995.1060