Existence of Independent Random Matching

Abstract

This paper shows the existence of independent random matching of a large (continuum) population in both static and dynamic systems, suitable for applications of the exact law of large numbers for random matching that have been popular in the economics and ge-netics literatures. We construct a joint agent-probability space, and randomized mutation, partial matching, and match-induced type-changing functions that satisfy appropriate in-dependence conditions. The proofs are achieved via nonstandard analysis. The proof for the dynamic setting relies on a new Fubini-type theorem for Loeb transition probabilities and their products, 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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