Laws of Large Numbers for Dynamical Systems with Randomly Matched Individuals

Abstract

Biologists and economists have analyzed populations where each individual interacts with randomly selected individuals. The random matching generates a very complicated stochastic system. Consequently biologists and economists have approximated such a system with a deterministic system. The justitication for such an approximation is that the population is assumed to be very large and thus some law of large numbers must hold. This paper gives a characterization of random matching schemes for countably infinite populations. In particular this paper shows that there exists a random matching scheme such that the stochastic system and the deterministic system are the same. Finally, we show that if the process lasts finitely many periods and if the population is large enough then the deterministic model offers a good approximation of the stochastic model. In doing so we make precise what we mean by population, matching process, and evolution of the population.

Additional Information

This paper could not have been written without the help of Roko Aliprantis and especially Kim Border. I would also like to thank for their help: Mahmoud El-Gamal, Richard McKelvey, Thomas Wolff. Financial support as provided by the John Randolph Haynes and Dora Haynes Fellowship and the Alfred P. Sloan Dissertation Fellowship and is duly appreciated. Published as Boylan, Richard T. "Laws of large numbers for dynamical systems with randomly matched individuals." Journal of Economic Theory 57, no. 2 (1992): 473-504.

Attached Files

Submitted - sswp748.pdf

Files

Additional details