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Existence of independent random matching

Darrell Duffie·Yeneng Sun
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Abstract

This paper shows the existence of independent random matching of a large (continuum) population in both static and dynamic systems, which has been popular in the economics and genetics literatures. We construct a joint agent-probability space, and randomized mutation, partial matching and match-induced type-changing functions that satisfy appropriate independence conditions. The proofs are achieved via nonstandard analysis. The proof for the dynamic setting relies on a new Fubini-type theorem for an infinite product of Loeb transition probabilities, based on which a continuum of independent Markov chains is derived from random mutation, random partial matching and random type changing.

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Darrell Duffie, Yeneng Sun. 2007-03-01. Existence of independent random matching. https://doi.org/10.1214/105051606000000673

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