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Title: The exact law of large numbers for independent random matching
Authors: Duffie, D.
Sun, Y. 
Keywords: Exact law of large numbers
Independent random matching
Population dynamics
Random mutation
Issue Date: May-2012
Citation: Duffie, D., Sun, Y. (2012-05). The exact law of large numbers for independent random matching. Journal of Economic Theory 147 (3) : 1105-1139. ScholarBank@NUS Repository.
Abstract: This paper provides a mathematical foundation for independent random matching of a large population, as widely used in the economics literature. We consider both static and dynamic systems with random mutation, partial matching arising from search, and type changes induced by matching. Under independence assumptions at each randomization step, we show that there is an almost-sure constant cross-sectional distribution of types in a large population, and moreover that the multi-period cross-sectional distribution of types is deterministic and evolves according to the transition matrices of the type process of a given agent. We also show the existence of a joint agent-probability space, and randomized mutation, partial matching and match-induced type-changing functions that satisfy appropriate independence conditions, where the agent space is an extension of the classical Lebesgue unit interval. © 2012.
Source Title: Journal of Economic Theory
ISSN: 00220531
DOI: 10.1016/j.jet.2012.01.003
Appears in Collections:Staff Publications

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