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The Distribution of Species Numbers in a Controlled Environment

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Summary

A model is proposed in which a population of projects is induced to distribute itself optimally over a number of modes (‘species’), consistently with resource constraints, by manipulation of a price vector. A control rule for the price vector is suggested which is shown by the use of a Liapunov function to achieve convergence to the optimum. For a stochastic version of the problem this Liapunov function has a distributional interpretation, leading to the conclusion that the numbers in the various surviving modes are distributed as independent gamma variables in an open model.
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Keywords: control by price; restless bandits; species distribution

Document Type: Research Article

Affiliations: Statistical Laboratory, Centre for Mathematical Sciences, Cambridge, UK

Publication date: March 1, 2004

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